0.13/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.15	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.15/0.37	% Computer   : n004.cluster.edu
0.15/0.37	% Model      : x86_64 x86_64
0.15/0.37	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.37	% Memory     : 8042.1875MB
0.15/0.37	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.37	% CPULimit   : 1200
0.15/0.37	% WCLimit    : 120
0.15/0.37	% DateTime   : Tue Jul 13 16:48:54 EDT 2021
0.15/0.37	% CPUTime    : 
254.11/32.38	% SZS status Theorem
254.11/32.38	
254.29/32.41	% SZS output start Proof
254.29/32.41	Take the following subset of the input axioms:
254.29/32.41	  fof(arity_HOL__Obool__Groups_Ominus, axiom, class_Groups_Ominus(tc_HOL_Obool)).
254.29/32.41	  fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot, axiom, class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)).
254.29/32.41	  fof(arity_HOL__Obool__Orderings_Obot, axiom, class_Orderings_Obot(tc_HOL_Obool)).
254.29/32.41	  fof(arity_HOL__Obool__Orderings_Oord, axiom, class_Orderings_Oord(tc_HOL_Obool)).
254.29/32.41	  fof(arity_HOL__Obool__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_HOL_Obool)).
254.29/32.41	  fof(conj_0, hypothesis, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))).
254.29/32.41	  fof(conj_1, conjecture, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))).
254.29/32.41	  fof(fact_Pi__I, axiom, ![T_a, T_b, V_B_2, V_A_2, V_f_2]: (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, V_B_2))) <= ![B_x]: (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), hAPP(V_B_2, B_x))) <= hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))).
254.29/32.41	  fof(fact_Prof__def, axiom, c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))=c_Arrow__Order__Mirabelle_OProf).
254.29/32.41	  fof(fact_mem__def, axiom, ![T_a, V_A_2, V_x_2]: (hBOOL(hAPP(hAPP(c_member(T_a), V_x_2), V_A_2)) <=> hBOOL(hAPP(V_A_2, V_x_2)))).
254.29/32.41	  fof(help_c__COMBK__1, axiom, ![T_a, T_b, V_Q, V_P]: hAPP(c_COMBK(T_a, T_b, V_P), V_Q)=V_P).
254.29/32.41	
254.29/32.41	Now clausify the problem and encode Horn clauses using encoding 3 of
254.29/32.41	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
254.29/32.41	We repeatedly replace C & s=t => u=v by the two clauses:
254.29/32.41	  fresh(y, y, x1...xn) = u
254.29/32.41	  C => fresh(s, t, x1...xn) = v
254.29/32.41	where fresh is a fresh function symbol and x1..xn are the free
254.29/32.41	variables of u and v.
254.29/32.41	A predicate p(X) is encoded as p(X)=true (this is sound, because the
254.29/32.41	input problem has no model of domain size 1).
254.29/32.41	
254.29/32.41	The encoding turns the above axioms into the following unit equations and goals:
254.29/32.41	
254.29/32.41	Axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot): class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) = true2.
254.29/32.41	Axiom 2 (arity_HOL__Obool__Groups_Ominus): class_Groups_Ominus(tc_HOL_Obool) = true2.
254.29/32.41	Axiom 3 (arity_HOL__Obool__Orderings_Obot): class_Orderings_Obot(tc_HOL_Obool) = true2.
254.29/32.41	Axiom 4 (arity_HOL__Obool__Orderings_Oord): class_Orderings_Oord(tc_HOL_Obool) = true2.
254.29/32.41	Axiom 5 (arity_HOL__Obool__Orderings_Oorder): class_Orderings_Oorder(tc_HOL_Obool) = true2.
254.29/32.41	Axiom 6 (fact_mem__def_1): fresh142(X, X, Y, Z) = true2.
254.29/32.41	Axiom 7 (fact_mem__def): fresh143(X, X, Y, Z, W) = true2.
254.29/32.41	Axiom 8 (help_c__COMBK__1): hAPP(c_COMBK(X, Y, Z), W) = Z.
254.29/32.41	Axiom 9 (fact_in__mono): fresh222(X, X, Y, Z, W, V) = hBOOL(hAPP(hAPP(c_member(V), Y), Z)).
254.29/32.41	Axiom 10 (fact_Pi__I_1): fresh405(X, X, Y, Z, W, V, U) = true2.
254.29/32.41	Axiom 11 (fact_mem__def): fresh143(hBOOL(hAPP(X, Y)), true2, X, Y, Z) = hBOOL(hAPP(hAPP(c_member(Z), Y), X)).
254.29/32.41	Axiom 12 (fact_extensional__funcset__mem): fresh243(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), Z)).
254.29/32.41	Axiom 13 (fact_mem__def_1): fresh142(hBOOL(hAPP(hAPP(c_member(X), Y), Z)), true2, Z, Y) = hBOOL(hAPP(Z, Y)).
254.29/32.41	Axiom 14 (fact_PiE): fresh407(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), hAPP(Z, Y))).
254.29/32.41	Axiom 15 (conj_0): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)) = true2.
254.29/32.41	Axiom 16 (fact_Prof__def): c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)) = c_Arrow__Order__Mirabelle_OProf.
254.29/32.41	Axiom 17 (fact_Pi__I_1): fresh405(hBOOL(hAPP(hAPP(c_member(X), hAPP(Y, b_x6(Z, Y, X, W, V))), hAPP(Z, b_x6(Z, Y, X, W, V)))), true2, Z, Y, X, W, V) = hBOOL(hAPP(hAPP(c_member(tc_fun(V, X)), Y), c_FuncSet_OPi(V, X, W, Z))).
254.29/32.41	
254.29/32.41	Lemma 18: class_Groups_Ominus(tc_HOL_Obool) = class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
254.29/32.41	Proof:
254.29/32.41	  class_Groups_Ominus(tc_HOL_Obool)
254.29/32.41	= { by axiom 2 (arity_HOL__Obool__Groups_Ominus) }
254.29/32.41	  true2
254.29/32.41	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.41	  class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
254.29/32.41	
254.29/32.41	Lemma 19: class_Orderings_Obot(tc_HOL_Obool) = class_Groups_Ominus(tc_HOL_Obool).
254.29/32.41	Proof:
254.29/32.41	  class_Orderings_Obot(tc_HOL_Obool)
254.29/32.41	= { by axiom 3 (arity_HOL__Obool__Orderings_Obot) }
254.29/32.41	  true2
254.29/32.41	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.41	  class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
254.29/32.41	= { by lemma 18 R->L }
254.29/32.41	  class_Groups_Ominus(tc_HOL_Obool)
254.29/32.41	
254.29/32.41	Lemma 20: class_Orderings_Oord(tc_HOL_Obool) = class_Orderings_Obot(tc_HOL_Obool).
254.29/32.41	Proof:
254.29/32.41	  class_Orderings_Oord(tc_HOL_Obool)
254.29/32.41	= { by axiom 4 (arity_HOL__Obool__Orderings_Oord) }
254.29/32.41	  true2
254.29/32.41	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.41	  class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
254.29/32.41	= { by lemma 18 R->L }
254.29/32.41	  class_Groups_Ominus(tc_HOL_Obool)
254.29/32.41	= { by lemma 19 R->L }
254.29/32.41	  class_Orderings_Obot(tc_HOL_Obool)
254.29/32.41	
254.29/32.41	Lemma 21: class_Orderings_Oorder(tc_HOL_Obool) = class_Orderings_Oord(tc_HOL_Obool).
254.29/32.41	Proof:
254.29/32.41	  class_Orderings_Oorder(tc_HOL_Obool)
254.29/32.41	= { by axiom 5 (arity_HOL__Obool__Orderings_Oorder) }
254.29/32.41	  true2
254.29/32.41	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.41	  class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
254.29/32.41	= { by lemma 18 R->L }
254.29/32.41	  class_Groups_Ominus(tc_HOL_Obool)
254.29/32.41	= { by lemma 19 R->L }
254.29/32.41	  class_Orderings_Obot(tc_HOL_Obool)
254.29/32.41	= { by lemma 20 R->L }
254.29/32.41	  class_Orderings_Oord(tc_HOL_Obool)
254.29/32.41	
254.29/32.41	Lemma 22: fresh222(X, X, hAPP(Y, Z), W, V, U) = fresh243(T, T, Z, W, S, Y, U, X2).
254.29/32.41	Proof:
254.29/32.41	  fresh222(X, X, hAPP(Y, Z), W, V, U)
254.29/32.41	= { by axiom 9 (fact_in__mono) }
254.29/32.41	  hBOOL(hAPP(hAPP(c_member(U), hAPP(Y, Z)), W))
254.29/32.41	= { by axiom 12 (fact_extensional__funcset__mem) R->L }
254.29/32.41	  fresh243(T, T, Z, W, S, Y, U, X2)
254.29/32.41	
254.29/32.41	Lemma 23: fresh243(X, X, Y, hAPP(Z, Y), W, V, U, T) = fresh407(S, S, Y, Z, X2, V, U, Y2).
254.29/32.41	Proof:
254.29/32.41	  fresh243(X, X, Y, hAPP(Z, Y), W, V, U, T)
254.29/32.42	= { by lemma 22 R->L }
254.29/32.42	  fresh222(Z2, Z2, hAPP(V, Y), hAPP(Z, Y), W2, U)
254.29/32.42	= { by axiom 9 (fact_in__mono) }
254.29/32.42	  hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), hAPP(Z, Y)))
254.29/32.42	= { by axiom 14 (fact_PiE) R->L }
254.29/32.42	  fresh407(S, S, Y, Z, X2, V, U, Y2)
254.29/32.42	
254.29/32.42	Goal 1 (conj_1): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf)) = true2.
254.29/32.42	Proof:
254.29/32.42	  hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))
254.29/32.42	= { by axiom 16 (fact_Prof__def) R->L }
254.29/32.42	  hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))))
254.29/32.42	= { by axiom 17 (fact_Pi__I_1) R->L }
254.29/32.42	  fresh405(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi))), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)))), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 9 (fact_in__mono) R->L }
254.29/32.42	  fresh405(fresh222(X, X, hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), Y, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 22 }
254.29/32.42	  fresh405(fresh243(Z, Z, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), W, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), V), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 23 }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), true2, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 18 R->L }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), class_Groups_Ominus(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 19 R->L }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), class_Orderings_Obot(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 20 R->L }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), class_Orderings_Oord(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 21 R->L }
254.29/32.42	  fresh405(fresh407(U, U, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), T, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), S), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 23 R->L }
254.29/32.42	  fresh405(fresh243(X2, X2, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), Y2, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), Z2), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 8 (help_c__COMBK__1) }
254.29/32.42	  fresh405(fresh243(X2, X2, b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi), c_Arrow__Order__Mirabelle_OLin, Y2, c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), Z2), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 22 R->L }
254.29/32.42	  fresh405(fresh222(W2, W2, hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), b_x6(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)), c_Arrow__Order__Mirabelle_OLin, V2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 8 (help_c__COMBK__1) }
254.29/32.42	  fresh405(fresh222(W2, W2, v_L, c_Arrow__Order__Mirabelle_OLin, V2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 9 (fact_in__mono) }
254.29/32.42	  fresh405(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 11 (fact_mem__def) R->L }
254.29/32.42	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), true2, c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.42	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 18 R->L }
254.29/32.42	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), class_Groups_Ominus(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.42	= { by lemma 19 R->L }
254.29/32.43	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), class_Orderings_Obot(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 20 R->L }
254.29/32.43	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), class_Orderings_Oord(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 21 R->L }
254.29/32.43	  fresh405(fresh143(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin, v_L)), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 13 (fact_mem__def_1) R->L }
254.29/32.43	  fresh405(fresh143(fresh142(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), true2, c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 9 (fact_in__mono) R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), true2, c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 18 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Groups_Ominus(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 19 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Obot(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 20 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oord(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 21 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(fresh222(U2, U2, v_L, c_Arrow__Order__Mirabelle_OLin, T2, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 9 (fact_in__mono) }
254.29/32.43	  fresh405(fresh143(fresh142(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 15 (conj_0) }
254.29/32.43	  fresh405(fresh143(fresh142(true2, class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.43	  fresh405(fresh143(fresh142(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 18 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(class_Groups_Ominus(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 19 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(class_Orderings_Obot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 20 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(class_Orderings_Oord(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 21 R->L }
254.29/32.43	  fresh405(fresh143(fresh142(class_Orderings_Oorder(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 6 (fact_mem__def_1) }
254.29/32.43	  fresh405(fresh143(true2, class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.43	  fresh405(fresh143(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 18 R->L }
254.29/32.43	  fresh405(fresh143(class_Groups_Ominus(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 19 R->L }
254.29/32.43	  fresh405(fresh143(class_Orderings_Obot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 20 R->L }
254.29/32.43	  fresh405(fresh143(class_Orderings_Oord(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 21 R->L }
254.29/32.43	  fresh405(fresh143(class_Orderings_Oorder(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_Arrow__Order__Mirabelle_OLin, v_L, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 7 (fact_mem__def) }
254.29/32.43	  fresh405(true2, class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 1 (arity_HOL__Obool__Lattices_Obounded__lattice__bot) R->L }
254.29/32.43	  fresh405(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 18 R->L }
254.29/32.43	  fresh405(class_Groups_Ominus(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 19 R->L }
254.29/32.43	  fresh405(class_Orderings_Obot(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 20 R->L }
254.29/32.43	  fresh405(class_Orderings_Oord(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by lemma 21 R->L }
254.29/32.43	  fresh405(class_Orderings_Oorder(tc_HOL_Obool), class_Orderings_Oorder(tc_HOL_Obool), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi)
254.29/32.43	= { by axiom 10 (fact_Pi__I_1) }
254.29/32.43	  true2
254.29/32.43	% SZS output end Proof
254.29/32.43	
254.29/32.43	RESULT: Theorem (the conjecture is true).
254.29/32.48	EOF