Nuprl Lemma : A-pre-val_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[A:Arr(AType)]. ∀[i:ℕn]. (A-pre-val(AType;A;i) ∈ Val)
Proof
Definitions occuring in Statement :
Arr: Arr(AType),
array: array{i:l}(Val;n),
A-pre-val: A-pre-val(AType;A;i),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
A-pre-val: A-pre-val(AType;A;i),
nat: ℕ
Lemmas referenced :
idx_wf,
int_seg_wf,
Arr_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[A:Arr(AType)]. \mforall{}[i:\mBbbN{}n].
(A-pre-val(AType;A;i) \mmember{} Val)
Date html generated:
2016_05_15-PM-02_19_13
Last ObjectModification:
2015_12_27-AM-08_58_24
Theory : monads
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