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
Definitions unfolded in proof :
top: Top,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
prop: ℙ,
glues: g glues Ia ──f⟶ Ib,
member: t ∈ T,
exists: ∃x:A. B[x],
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb,
glued: glued(es;B;f;Ia;Ib),
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
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:
2016_05_17-AM-08_00_43
Last ObjectModification:
2015_12_28-PM-11_20_37
Theory : event-ordering
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