Nuprl Lemma : p-restrict_wf

[A,B:Type]. ∀[f:A ⟶ (B Top)]. ∀[P:A ⟶ ℙ]. ∀[p:∀x:A. Dec(P[x])].  (p-restrict(f;p) ∈ A ⟶ (B Top))


Proof




Definitions occuring in Statement :  p-restrict: p-restrict(f;p) decidable: Dec(P) uall: [x:A]. B[x] top: Top prop: so_apply: x[s] all: x:A. B[x] member: t ∈ T function: x:A ⟶ B[x] union: left right universe: Type
Definitions unfolded in proof :  p-restrict: p-restrict(f;p) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] so_apply: x[s] prop:
Lemmas referenced :  p-compose_wf p-filter_wf all_wf decidable_wf top_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality cumulativity universeEquality unionEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  (B  +  Top)].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[p:\mforall{}x:A.  Dec(P[x])].
    (p-restrict(f;p)  \mmember{}  A  {}\mrightarrow{}  (B  +  Top))



Date html generated: 2016_05_15-PM-03_31_14
Last ObjectModification: 2015_12_27-PM-01_10_56

Theory : general


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