Nuprl Lemma : es-is-interface-co-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].
uiff(↑e ∈b (I|¬p);(↑e ∈b I) ∧ (¬P[es;e]))
Proof
Definitions occuring in Statement :
es-interface-co-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),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-co-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,
eq_int: (i =z j),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
not: ¬A,
eclass: EClass(A[eo; e]),
nat: ℕ,
so_lambda: λ2x y.t[x; y],
top: Top
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].
uiff(\muparrow{}e \mmember{}\msubb{} (I|\mneg{}p);(\muparrow{}e \mmember{}\msubb{} I) \mwedge{} (\mneg{}P[es;e]))
Date html generated:
2016_05_16-PM-10_46_55
Last ObjectModification:
2015_12_29-AM-10_51_22
Theory : event-ordering
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