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
Home
Index