Nuprl Lemma : vr_RAC2_implies_GRAC
(
A,B:Type. R:A 
B 
.
((x:A. 
y:B. (R x y)) 
(R':A B . ((R' <= R 
R <= R') (x:A. !y:B. R' x y)))))
vr_GRAC
Proof not projected
Definitions occuring in Statement :
vr_GRAC: vr_GRAC,
vr_sub-rel: R1 <= R2,
vr_exists_uni: !x:T. P[x],
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
product: x:A 
B[x],
lambda: 
x.A[x],
spread: spread def,
apply: f a,
Auto: Error :Auto,
D: Error :D,
all: x:A. B[x],
function: x:A B[x],
universe: Type,
prop: ,
exists: x:A. B[x],
vr_sub-rel: R1 <= R2,
and: P Q,
so_lambda: 
x.t[x],
vr_exists_uni: !x:T. P[x],
implies: P Q,
vr_GRAC: vr_GRAC,
member: t 
T,
equal: s = t,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
natural_number: $n,
subtype_rel: A 
r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
pair: <a, b>,
Unfold: Error :Unfold,
limited-type: LimitedType,
BHyp: Error :BHyp
Lemmas :
vr_exists_uni_wf,
vr_sub-rel_wf
(\mforall{}A,B:Type. \mforall{}R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}.
((\mforall{}x:A. \mexists{}y:B. (R x y)) {}\mRightarrow{} (\mexists{}R':A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}. ((R' <= R \mwedge{} R <= R') \mwedge{} (\mforall{}x:A. \mexists{}!y:B. R' x y)))))
{}\mRightarrow{} vr\_GRAC
Date html generated:
2012_02_20-PM-03_35_06
Last ObjectModification:
2012_02_02-PM-01_55_41
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