Nuprl Lemma : classfun-res-eclass3

[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  (eclass3(X;Y)@e (X@e Y@e) ∈ C) supposing (X is functional at and is functional at e)


Proof




Definitions occuring in Statement :  eclass3: eclass3(X;Y) classfun-res: X@e es-functional-class-at: is functional at e eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E uimplies: supposing a uall: [x:A]. B[x] apply: a function: x:A ⟶ B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a classfun-res: X@e eclass3: eclass3(X;Y) classfun: X(e) class-ap: X(e) eclass: EClass(A[eo; e]) so_lambda: λ2x.t[x] so_apply: x[s] es-functional-class-at: is functional at e implies:  Q and: P ∧ Q iff: ⇐⇒ Q all: x:A. B[x] top: Top prop: subtype_rel: A ⊆B so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] guard: {T} rev_implies:  Q

Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  C)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    (eclass3(X;Y)@e  =  (X@e  Y@e))  supposing  (X  is  functional  at  e  and  Y  is  functional  at  e)



Date html generated: 2016_05_17-AM-11_16_34
Last ObjectModification: 2015_12_29-PM-05_13_37

Theory : process-model


Home Index