Nuprl Lemma : es-interface-restrict-trivial
∀[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E. Dec(P[es;e])].
(I|p) = I ∈ EClass(A) supposing ∀es:EO+(Info). ∀e:E. ((¬P[es;e]) ⇒ ((I es e) = {} ∈ bag(A)))
Proof
Definitions occuring in Statement :
es-interface-restrict: (I|p),
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 :
all_wf,
decidable_wf,
bag_wf,
empty-bag_wf,
iff_weakening_equal,
equal_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
not_wf,
equal-wf-T-base,
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])].
(I|p) = I supposing \mforall{}es:EO+(Info). \mforall{}e:E. ((\mneg{}P[es;e]) {}\mRightarrow{} ((I es e) = \{\}))
Date html generated:
2015_07_20-PM-03_30_25
Last ObjectModification:
2015_02_04-PM-05_27_55
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