:: SCHEMS_1 semantic presentation
scheme
:: SCHEMS_1:sch 4
s4{
P
1
[
set
] } :
ex
a
being
set
st
P
1
[
a
]
provided
E6
: for
a
being
set
holds
P
1
[
a
]
proof
end;
scheme
:: SCHEMS_1:sch 7
s7{
P
1
[
set
,
set
] } :
for
b
being
set
ex
a
being
set
st
P
1
[
a
,
b
]
provided
E6
: ex
a
being
set
st
for
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 10
s10{
P
1
[
set
],
P
2
[
set
] } :
( ( for
a
being
set
holds
P
1
[
a
] ) implies for
a
being
set
holds
P
2
[
a
] )
provided
E6
: for
a
being
set
st
P
1
[
a
] holds
P
2
[
a
]
proof
end;
scheme
:: SCHEMS_1:sch 12
s12{
P
1
[
set
],
P
2
[
set
] } :
( ( for
a
being
set
holds
P
1
[
a
] ) iff for
a
being
set
holds
P
2
[
a
] )
provided
E6
: for
a
being
set
holds
(
P
1
[
a
] iff
P
2
[
a
] )
proof
end;
scheme
:: SCHEMS_1:sch 14
s14{
P
1
[
set
],
P
2
[] } :
( ( for
a
being
set
holds
P
1
[
a
] ) implies
P
2
[] )
provided
E6
: for
a
being
set
st
P
1
[
a
] holds
P
2
[]
proof
end;
scheme
:: SCHEMS_1:sch 16
s16{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
provided
E6
: ( ex
a
being
set
st
P
1
[
a
] or for
b
being
set
holds
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 18
s18{
P
1
[
set
],
P
2
[
set
] } :
( ex
a
being
set
st
P
1
[
a
] or for
b
being
set
holds
P
2
[
b
] )
provided
E6
: ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 19
s19{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] or
P
2
[
b
] )
provided
E6
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] or
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 20
s20{
P
1
[
set
],
P
2
[
set
] } :
for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
provided
E6
: ( ex
a
being
set
st
P
1
[
a
] & ( for
b
being
set
holds
P
2
[
b
] ) )
proof
end;
scheme
:: SCHEMS_1:sch 21
s21{
P
1
[
set
],
P
2
[
set
] } :
( ex
a
being
set
st
P
1
[
a
] & ( for
b
being
set
holds
P
2
[
b
] ) )
provided
E6
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 24
s24{
P
1
[
set
],
P
2
[
set
] } :
ex
a
being
set
st
for
b
being
set
holds
(
P
1
[
a
] &
P
2
[
b
] )
provided
E6
: for
b
being
set
ex
a
being
set
st
(
P
1
[
a
] &
P
2
[
b
] )
proof
end;
scheme
:: SCHEMS_1:sch 25
s25{
P
1
[
set
,
set
] } :
ex
b
being
set
st
for
a
being
set
holds
P
1
[
a
,
b
]
provided
E6
: for
a
,
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 26
s26{
P
1
[
set
,
set
] } :
ex
a
being
set
st
P
1
[
a
,
a
]
provided
E6
: ex
a
being
set
st
for
b
being
set
holds
P
1
[
a
,
b
]
proof
end;
scheme
:: SCHEMS_1:sch 27
s27{
P
1
[
set
,
set
] } :
for
a
being
set
ex
b
being
set
st
P
1
[
b
,
a
]
provided
E6
: for
a
being
set
holds
P
1
[
a
,
a
]
proof
end;
scheme
:: SCHEMS_1:sch 28
s28{
P
1
[
set
,
set
] } :
for
a
being
set
ex
b
being
set
st
P
1
[
a
,
b
]
provided
E6
: for
a
being
set
holds
P
1
[
a
,
a
]
proof
end;
scheme
:: SCHEMS_1:sch 29
s29{
P
1
[
set
,
set
] } :
ex
a
,
b
being
set
st
P
1
[
a
,
b
]
provided
E6
: for
b
being
set
ex
a
being
set
st
P
1
[
a
,
b
]
proof
end;