:: SCHEMS_1 semantic presentation
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scheme
:: SCHEMS_1:sch 1
Schemat0
{
P
1
[
set
] } :
ex
a
being
set
st
P
1
[
a
]
provided
A1
: for
a
being
set
holds
P
1
[
a
]
proof
end;
scheme
:: SCHEMS_1:sch 2
Schemat3
{
P
1
[
set
,
set
] } :
for
b
being
set
ex
a
being
set
st
P
1
[
a
,
b
]
provided
A1
: ex
a
being
set
st
for
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 3
Schemat8
{
P
1
[
set
],
P
2
[
set
] } :
( ( for
a
being
set
holds
P
1
[
a
] ) implies for
a
being
set
holds
P
2
[
a
] )
provided
A1
: for
a
being
set
st
P
1
[
a
] holds
P
2
[
a
]
proof
end;
scheme
:: SCHEMS_1:sch 4
Schemat9
{
P
1
[
set
],
P
2
[
set
] } :
( ( for
a
being
set
holds
P
1
[
a
] ) iff for
a
being
set
holds
P
2
[
a
] )
provided
A1
: for
a
being
set
holds
(
P
1
[
a
] iff
P
2
[
a
] )
proof
end;
scheme
:: SCHEMS_1:sch 5
Schemat17
{
P
1
[
set
],
P
2
[] } :
( ( for
a
being
set
holds
P
1
[
a
] ) implies
P
2
[] )
provided
A1
: for
a
being
set
st
P
1
[
a
] holds
P
2
[]
proof
end;
scheme
:: SCHEMS_1:sch 6
Schemat18a
{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
provided
A1
: ( ex
a
being
set
st
P
1
[
a
] or for
b
being
set
holds
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 7
Schemat18b
{
P
1
[
set
],
P
2
[
set
] } :
( ex
a
being
set
st
P
1
[
a
] or for
b
being
set
holds
P
2
[
b
] )
provided
A1
: ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 8
Schemat20b
{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
provided
A1
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] or
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 9
Schemat22a
{
P
1
[
set
],
P
2
[
set
] } :
for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
provided
A1
: ( ex
a
being
set
st
P
1
[
a
] & ( for
b
being
set
holds
P
2
[
b
] ) )
proof
end;
scheme
:: SCHEMS_1:sch 10
Schemat22b
{
P
1
[
set
],
P
2
[
set
] } :
( ex
a
being
set
st
P
1
[
a
] & ( for
b
being
set
holds
P
2
[
b
] ) )
provided
A1
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 11
Schemat23b
{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] &
P
2
[
b
] )
provided
A1
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 12
Schemat28
{
P
1
[
set
,
set
] } :
ex
b
being
set
st
for
a
being
set
holds
P
1
[
a
,
b
]
provided
A1
: for
a
,
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 13
Schemat30
{
P
1
[
set
,
set
] } :
ex
a
being
set
st
P
1
[
a
,
a
]
provided
A1
: ex
a
being
set
st
for
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 14
Schemat31
{
P
1
[
set
,
set
] } :
for
a
being
set
ex
b
being
set
st
P
1
[
b
,
a
]
provided
A1
: for
a
being
set
holds
P
1
[
a
,
a
]
proof
end;
scheme
:: SCHEMS_1:sch 15
Schemat33
{
P
1
[
set
,
set
] } :
for
a
being
set
ex
b
being
set
st
P
1
[
a
,
b
]
provided
A1
: for
a
being
set
holds
P
1
[
a
,
a
]
proof
end;
scheme
:: SCHEMS_1:sch 16
Schemat36
{
P
1
[
set
,
set
] } :
ex
a
,
b
being
set
st
P
1
[
a
,
b
]
provided
A1
: for
b
being
set
ex
a
being
set
st
P
1
[
a
,
b
]
proof
end;