Nuprl Lemma : apply-partial-indep
∀[A,B:Type]. ∀[f:partial(A ⟶ B)]. ∀[a:A]. f a ∈ partial(B) supposing value-type(B)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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,
hypothesisEquality,
independent_isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:partial(A {}\mrightarrow{} B)]. \mforall{}[a:A]. f a \mmember{} partial(B) supposing value-type(B)
Date html generated:
2016_05_14-AM-06_10_19
Last ObjectModification:
2015_12_26-AM-11_51_56
Theory : partial_1
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