Nuprl Lemma : A-post-val_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[prog:A-map Unit]. ∀[A:Arr(AType)]. ∀[i:ℕn].
(A-post-val(AType;prog;A;i) ∈ Val)
Proof
Definitions occuring in Statement :
A-post-val: A-post-val(AType;prog;A;i),
A-map: A-map,
array-model: array-model(AType),
Arr: Arr(AType),
array: array{i:l}(Val;n),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
apply: f a,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
A-post-val: A-post-val(AType;prog;A;i),
nat: ℕ,
subtype_rel: A ⊆r B
Lemmas referenced :
int_seg_wf,
Arr_wf,
A-map_wf,
unit_wf2,
array_wf,
nat_wf,
A-eval_wf,
A-coerce_wf,
A-map'_wf,
A-fetch'_wf,
A-bind_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
because_Cache,
applyEquality,
universeEquality,
lambdaEquality,
isectEquality,
cumulativity,
functionEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[prog:A-map Unit]. \mforall{}[A:Arr(AType)]. \mforall{}[i:\mBbbN{}n].
(A-post-val(AType;prog;A;i) \mmember{} Val)
Date html generated:
2016_05_15-PM-02_19_11
Last ObjectModification:
2015_12_27-AM-08_58_28
Theory : monads
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