Nuprl Lemma : Q-R-glues-trivial-restrict
∀[Info:Type]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ].
∀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) = {} ∈ bag(B) supposing ¬P[es;e])
⇒ (∀es:EO+(Info)
∀[Q,R:E ─→ E ─→ ℙ].
∀f:E(Ia) ─→ B. ∀g:E(Ib) ─→ E. (g glues Ia:Q ──f─→ (Ib|p):R ⇒ g glues Ia:Q ──f─→ Ib:R)))
Proof
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: ℙ,
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 ∈ T,
empty-bag: {},
bag: bag(T)
Lemmas :
Q-R-glues_wf,
squash_wf,
true_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
eclass_wf,
event-ordering+_cumulative2,
es-interface-restrict-trivial,
bag_wf,
empty-bag_wf,
iff_weakening_equal,
not_wf,
subtype_rel_dep_function,
es-interface-restrict_wf,
es-E-interface-restrict,
subtype_rel_self,
all_wf,
isect_wf,
equal-wf-T-base,
decidable_wf
Latex:
\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:
2015_07_21-PM-04_11_14
Last ObjectModification:
2015_02_04-PM-06_04_27
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