Nuprl Lemma : A-fetch_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. (A-fetch(array-model(AType)) ∈ ℕn ⟶ (A-map Val))
Proof
Definitions occuring in Statement :
A-fetch: A-fetch(AModel),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
A-fetch: A-fetch(AModel),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
A-coerce_wf,
A-map'_wf,
A-map_wf,
A-fetch'_wf,
int_seg_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. (A-fetch(array-model(AType)) \mmember{} \mBbbN{}n {}\mrightarrow{} (A-map Val))
Date html generated:
2016_05_15-PM-02_18_56
Last ObjectModification:
2015_12_27-AM-08_58_35
Theory : monads
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