%------------------------------------------------------------------------------
% File     : GEO362^1 : TPTP v9.0.0. Released v7.0.0.
% Domain   : Geometry (Plane Geometry)
% Problem  : Chart System Math I+A Red Book, Problem 07CRAR098
% Version  : [Mat16] axioms : Especial.
% English  : 

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : Chart-1A-Red-07CRAR098.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 ( 728 unt;1199 typ;   0 def)
%            Number of atoms       : 6948 (2210 equ;   0 cnn)
%            Maximal formula atoms :   31 (   3 avg)
%            Number of connectives : 39618 ( 104   ~; 233   |;1174   &;35980   @)
%                                         (1095 <=>;1032  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   8 avg)
%            Number arithmetic     : 4463 ( 371 atm;1205 fun; 951 num;1936 var)
%            Number of types       :   40 (  36 usr;   3 ari)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1213 (1170 usr;  67 con; 0-9 aty)
%            Number of variables   : 8059 ( 405   ^;7089   !; 429   ?;8059   :)
%                                         ( 136  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Level: 2; Author: Munehiro Kobayashi;
%            Generated: 2014-12-23
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include('Axioms/MAT001^0.ax').
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thf(p,conjecture,
    ! [V_A: '2d.Point',V_B: '2d.Point',V_C: '2d.Point',V_H: '2d.Point'] :
      ( ( ( '2d.is-triangle/3' @ V_A @ V_B @ V_C )
        & ( '2d.is-right/1' @ ( '2d.angle/3' @ V_C @ V_A @ V_B ) )
        & ( V_H
          = ( '2d.foot-of-perpendicular-line-from-to/2' @ V_A @ ( '2d.line/2' @ V_B @ V_C ) ) ) )
     => ( ( $product @ ( '2d.distance^2/2' @ V_A @ V_B ) @ ( '2d.distance/2' @ V_C @ V_H ) )
        = ( $product @ ( '2d.distance^2/2' @ V_A @ V_C ) @ ( '2d.distance/2' @ V_B @ V_H ) ) ) ) ).

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