Nuprl Lemma : fun_with_inv_is_bij
13,42
postcript
pdf
A
,
B
:Type,
f
:(
A
B
),
g
:(
B
A
). InvFuns(
A
;
B
;
f
;
g
)
Bij(
A
;
B
;
f
)
latex
Up
fun
1
,
fun
1
Definitions
t
T
,
P
Q
,
x
:
A
.
B
(
x
)
,
,
Surj(
A
;
B
;
f
)
,
Inj(
A
;
B
;
f
)
,
P
&
Q
,
Bij(
A
;
B
;
f
)
,
x
:
A
.
B
(
x
)
,
InvFuns(
A
;
B
;
f
;
g
)
,
Id
,
Id{
T
}
,
f
o
g
Lemmas
inv
funs
wf
origin
A, B:Type, f:(A
B), g:(BA). InvFuns(A;B;f;g) 
Bij(A;B;f) A, B:Type, f:(AB), g:(BA). InvFuns(A;B;f;g) Bij(A;B;f) 
T Qx:A. B(x)
x:A. B(x)