Nuprl Lemma : es-E-interface-restrict
∀[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E. Dec(P[es;e])]. ∀[es:EO+(Info)].
(E((I|p)) ⊆r E(I))
Proof
Definitions occuring in Statement :
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),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-E-interface_functionality,
es-interface-restrict_wf,
top_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
es-is-interface-restrict,
assert_wf,
in-eclass_wf,
event-ordering+_wf,
all_wf,
decidable_wf,
eclass_wf
Latex:
\mforall{}[Info,A:Type]. \mforall{}[I:EClass(A)]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}[p:\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P[es;e])]. \mforall{}[es:EO+(Info)].
(E((I|p)) \msubseteq{}r E(I))
Date html generated:
2015_07_20-PM-03_30_59
Last ObjectModification:
2015_01_27-PM-10_18_21
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