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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
eclass: EClass(A[eo; e])
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:
2016_05_17-AM-07_53_34
Last ObjectModification:
2016_01_17-PM-02_45_55
Theory : event-ordering
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