Nuprl Lemma : vr_SURJ_implies_RINV
[A,B:Type]. [f:A 
B]. (vr_SURJ(f;A;B) 
vr_RINV(f;A;B))
Proof not projected
Definitions occuring in Statement :
vr_RINV: vr_RINV(f;A;B),
vr_SURJ: vr_SURJ(f;A;B),
uall: [x:A]. B[x],
implies: P Q,
function: x:A B[x],
universe: Type
Definitions :
lambda: 
x.A[x],
equal: s = t,
apply: f a,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
function: x:A B[x],
all: x:A. B[x],
member: t 
T,
vr_SURJ: vr_SURJ(f;A;B),
universe: Type,
product: x:A 
B[x],
exists: 
x:A. B[x],
vr_RINV: vr_RINV(f;A;B),
implies: P Q,
vr_AC: vr_AC,
limited-type: LimitedType,
prop: 
,
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B)
Lemmas :
vr_AC_r,
vr_SURJ_wf
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. (vr\_SURJ(f;A;B) {}\mRightarrow{} vr\_RINV(f;A;B))
Date html generated:
2012_02_20-PM-03_34_42
Last ObjectModification:
2012_02_02-PM-01_55_37
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