Nuprl Lemma : A-eval_wf2
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T:Type]. ∀[m:A-map T]. ∀[A:Arr(AType)].
(A-eval(array-model(AType)) m A ∈ T)
Proof
Definitions occuring in Statement :
A-map: A-map,
array-model: array-model(AType),
Arr: Arr(AType),
array: array{i:l}(Val;n),
A-eval: A-eval(AModel),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
A-eval_wf,
A-map_wf,
Arr_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[T:Type]. \mforall{}[m:A-map T]. \mforall{}[A:Arr(AType)].
(A-eval(array-model(AType)) m A \mmember{} T)
Date html generated:
2016_05_15-PM-02_18_22
Last ObjectModification:
2015_12_27-AM-08_58_53
Theory : monads
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