Nuprl Lemma : simple-swap_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[i,j:ℕn]. (simple-swap(array-model(AType);i;j) ∈ A-map Unit)
Proof
Definitions occuring in Statement :
simple-swap: simple-swap(AModel;i;j),
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],
unit: Unit,
member: t ∈ T,
apply: f a,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
simple-swap: simple-swap(AModel;i;j),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
unit_wf2,
A-coerce_wf,
A-fetch'_wf,
A-assign_wf,
A-map'_wf,
A-map_wf,
int_seg_wf,
array_wf,
nat_wf,
A-bind_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
intEquality,
hypothesisEquality,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
applyEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
sqequalRule,
natural_numberEquality,
setElimination,
rename,
isect_memberFormation,
introduction,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)]. \mforall{}[i,j:\mBbbN{}n]. (simple-swap(array-model(AType);i;j) \mmember{} A-map Unit)
Date html generated:
2016_05_15-PM-02_20_12
Last ObjectModification:
2015_12_27-AM-08_59_08
Theory : monads
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