Nuprl Lemma : es-is-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:E. (↑e ∈b (I|p) ⇐⇒ (↑e ∈b I) ∧ P[es;e])
Proof
Definitions occuring in Statement :
es-interface-restrict: (I|p),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
in-eclass: e ∈b X,
es-interface-restrict: (I|p),
member: t ∈ T,
subtype_rel: A ⊆r B,
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
eclass: EClass(A[eo; e]),
nat: ℕ,
rev_implies: P ⇐ Q,
eq_int: (i =z j),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
not: ¬A,
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]). \mforall{}es:EO+(Info). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} (I|p) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} I) \mwedge{} P[es;e])
Date html generated:
2016_05_16-PM-10_46_16
Last ObjectModification:
2015_12_29-AM-10_50_52
Theory : event-ordering
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