Nuprl Lemma : A-bind2_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T,S:Type]. ∀[m:A-map T]. ∀[k:T ⟶ (A-map S)].
(m >> \x.
k[x] ∈ A-map S)
Proof
Definitions occuring in Statement :
A-bind2: A-bind2,
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
nat: ℕ,
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,
A-bind2: A-bind2,
so_apply: x[s]
Lemmas referenced :
A-bind_wf,
A-map_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[T,S:Type]. \mforall{}[m:A-map T]. \mforall{}[k:T {}\mrightarrow{} (A-map S)].
(m >> \mbackslash{}x.
k[x] \mmember{} A-map S)
Date html generated:
2016_05_15-PM-02_20_37
Last ObjectModification:
2015_12_27-AM-08_58_00
Theory : monads
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