Nuprl Lemma : glued-Q-R-glued
∀[Info:Type]
∀es:EO+(Info)
∀[A,B:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀f:E(Ia) ─→ B. (glued(es;B;f;Ia;Ib) ⇐⇒ Ia:λe,e'. e ≤loc e' →─f─→ Ib:λe,e'. e ≤lo\000Cc e' )
Proof
Definitions occuring in Statement :
glued: glued(es;B;f;Ia;Ib),
Q-R-glued: Ia:Qa →─f─→ Ib:Rb,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
Q-R-glues_wf,
glued_wf,
glues_wf,
Q-R-glued_wf,
es-le_wf,
event-ordering+_subtype,
es-E_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
eclass_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f:E(Ia) {}\mrightarrow{} B.
(glued(es;B;f;Ia;Ib) \mLeftarrow{}{}\mRightarrow{} Ia:\mlambda{}e,e'. e \mleq{}loc e' \mrightarrow{}{}f{}\mrightarrow{} Ib:\mlambda{}e,e'. e \mleq{}loc e' )
Date html generated:
2015_07_21-PM-04_15_05
Last ObjectModification:
2015_01_27-PM-05_43_52
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