### Nuprl Lemma : apply-bar

`∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:partial(a:A ⟶ B[a])]. ∀[a:A].  f a ∈ partial(B[a]) supposing value-type(B[a])`

Proof

Definitions occuring in Statement :  partial: `partial(T)` value-type: `value-type(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` apply: `f a` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  apply-partial value-type_wf partial_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache sqequalRule lambdaEquality applyEquality hypothesisEquality independent_isectElimination hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality functionEquality cumulativity universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f:partial(a:A  {}\mrightarrow{}  B[a])].  \mforall{}[a:A].
f  a  \mmember{}  partial(B[a])  supposing  value-type(B[a])

Date html generated: 2016_05_15-PM-10_04_39
Last ObjectModification: 2015_12_27-PM-05_16_47

Theory : bar!type

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