Documentation
Mathlib
.
Init
.
Propext
Search
Google site search
Mathlib
.
Init
.
Propext
source
Imports
Init
Mathlib.Init.Logic
Mathlib.Mathport.Rename
Imported by
imp_congr_eq
imp_congr_ctx_eq
eq_true_intro
eq_false_intro
Iff
.
to_eq
iff_eq_eq
Additional congruence lemmas.
source
theorem
imp_congr_eq
{a :
Prop
}
{b :
Prop
}
{c :
Prop
}
{d :
Prop
}
(h₁ :
a
=
c
)
(h₂ :
b
=
d
)
:
(
a
→
b
)
=
(
c
→
d
)
source
theorem
imp_congr_ctx_eq
{a :
Prop
}
{b :
Prop
}
{c :
Prop
}
{d :
Prop
}
(h₁ :
a
=
c
)
(h₂ :
c
→
b
=
d
)
:
(
a
→
b
)
=
(
c
→
d
)
source
theorem
eq_true_intro
{a :
Prop
}
(h :
a
)
:
a
=
True
source
theorem
eq_false_intro
{a :
Prop
}
(h :
¬
a
)
:
a
=
False
source
theorem
Iff
.
to_eq
{a :
Prop
}
{b :
Prop
}
(h :
a
↔
b
)
:
a
=
b
source
theorem
iff_eq_eq
{a :
Prop
}
{b :
Prop
}
:
(
a
↔
b
)
=
(
a
=
b
)