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 ⋂ 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: 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 ⋂ 0 all: x:A. B[x] not: ¬A implies:  Q false: False and: P ∧ Q uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] subtype_rel: A ⊆B iff: ⇐⇒ Q uiff: uiff(P;Q) uimplies: supposing a prop: 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


Home Index