Nuprl Lemma : es-interface-restrict-disjoint
∀[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|¬p) = 0
Proof
Definitions occuring in Statement :
es-interface-disjoint: X ⋂ Y = 0,
es-interface-co-restrict: (I|¬p),
es-interface-restrict: (I|p),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
es-interface-disjoint: X ⋂ Y = 0,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
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) \mcap{} (I|\mneg{}p) = 0
Date html generated:
2016_05_16-PM-10_50_08
Last ObjectModification:
2015_12_29-AM-10_49_01
Theory : event-ordering
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