Nuprl Lemma : fpf-restrict-compatible

[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:x:A fp-> B[x]].
  fpf-restrict(f;P) || supposing || g


Proof




Definitions occuring in Statement :  fpf-restrict: fpf-restrict(f;P) fpf-compatible: || g fpf: a:A fp-> B[a] deq: EqDecider(T) bool: 𝔹 uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  fpf-compatible: || g all: x:A. B[x] member: t ∈ T top: Top uall: [x:A]. B[x] uimplies: supposing a implies:  Q and: P ∧ Q cand: c∧ B so_lambda: λ2x.t[x] so_apply: x[s] uiff: uiff(P;Q) guard: {T} prop: subtype_rel: A ⊆B

Latex:
\mforall{}[A:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f,g:x:A  fp->  B[x]].
    fpf-restrict(f;P)  ||  g  supposing  f  ||  g



Date html generated: 2016_05_16-AM-11_34_03
Last ObjectModification: 2015_12_29-AM-09_30_02

Theory : event-ordering


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