Nuprl Lemma : simple-swap-test_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)].
let AModel = array-model(AType) in
∀[prog:A-map Unit]. ∀[i,j:ℕn]. (simple-swap-test(AModel;prog;i;j) ∈ A-map 𝔹)
Proof
Definitions occuring in Statement :
simple-swap-test: simple-swap-test(AModel;prog;i;j),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
let: let,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
apply: f a,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
nat: ℕ,
simple-swap-test: simple-swap-test(AModel;prog;i;j),
member: t ∈ T,
let: let,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
A-fetch'_wf,
A-coerce_wf,
A-bind_wf,
A-return_wf,
bool_wf,
band_wf,
eq_int_wf,
int_seg_wf,
A-map_wf,
unit_wf2,
array_wf,
nat_wf
Rules used in proof :
intEquality,
applyEquality,
because_Cache,
isect_memberEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
sqequalRule,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
lambdaEquality_alt,
inhabitedIsType,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality,
isectEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)].
let AModel = array-model(AType) in
\mforall{}[prog:A-map Unit]. \mforall{}[i,j:\mBbbN{}n]. (simple-swap-test(AModel;prog;i;j) \mmember{} A-map \mBbbB{})
Date html generated:
2020_05_20-AM-08_00_21
Last ObjectModification:
2020_01_17-AM-07_45_34
Theory : monads
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