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)
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
es-interface-restrict: (I|p),
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y]
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:
2016_05_16-PM-10_48_08
Last ObjectModification:
2016_01_17-PM-07_18_01
Theory : event-ordering
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