Nuprl Lemma : Q-R-glues-trivial-restrict
[Info:Type]. [P:es:EO+(Info) 
E 
].
p:es:EO+(Info). e:E. Dec(P[es;e])
[A,B:Type].
Ia:EClass(A). Ib:EClass(B).
((es:EO+(Info). e:E. (Ib es e) = {} supposing 
P[es;e])
(es:EO+(Info)
[Q,R:E E ].
f:E(Ia) B. g:E(Ib) E. (g glues Ia:Q f (Ib|p):R g glues Ia:Q f Ib:R)))
Proof not projected
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa f Ib:Rb,
es-interface-restrict: (I|p),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
not: A,
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
so_apply: x[s1;s2],
eclass: EClass(A[eo; e]),
implies: P Q,
uimplies: b supposing a,
member: t 
T,
so_lambda: 
x y.t[x; y],
subtype: S 
T,
suptype: suptype(S; T),
so_lambda: x.t[x],
true: True,
squash: 
T,
so_apply: x[s],
guard: {T}
Lemmas :
es-interface-restrict-trivial,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
not_wf,
Q-R-glues_wf,
es-interface-restrict_wf,
es-E-interface_wf,
es-interface-top,
all_wf,
isect_wf,
equal_wf,
bag_wf,
empty-bag_wf,
eclass_wf,
decidable_wf,
true_wf,
squash_wf,
top_wf
\mforall{}[Info:Type]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}p:\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P[es;e])
\mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B).
((\mforall{}es:EO+(Info). \mforall{}e:E. (Ib es e) = \{\} supposing \mneg{}P[es;e])
{}\mRightarrow{} (\mforall{}es:EO+(Info)
\mforall{}[Q,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}f:E(Ia) {}\mrightarrow{} B. \mforall{}g:E(Ib) {}\mrightarrow{} E.
(g glues Ia:Q {}{}f{}\mrightarrow{} (Ib|p):R {}\mRightarrow{} g glues Ia:Q {}{}f{}\mrightarrow{} Ib:R)))
Date html generated:
2012_01_23-PM-12_29_08
Last ObjectModification:
2011_12_17-PM-04_48_11
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