Nuprl Lemma : simple-swap-test2_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[prog:A-map Unit]. ∀[i,j,k:ℕn].
(simple-swap-test2(array-model(AType);prog;i;j;k) ∈ A-map 𝔹)
Proof
Definitions occuring in Statement :
simple-swap-test2: simple-swap-test2(AModel;prog;i;j;k),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
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-test2: simple-swap-test2(AModel;prog;i;j;k),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
int_seg: {i..j-},
bimplies: p ⇒b q
Lemmas referenced :
A-fetch'_wf,
A-coerce_wf,
A-map'_wf,
A-bind_wf,
A-return_wf,
bool_wf,
band_wf,
eq_int_wf,
bor_wf,
bnot_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,
sqequalRule,
cut,
introduction,
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)]. \mforall{}[prog:A-map Unit]. \mforall{}[i,j,k:\mBbbN{}n].
(simple-swap-test2(array-model(AType);prog;i;j;k) \mmember{} A-map \mBbbB{})
Date html generated:
2020_05_20-AM-08_00_32
Last ObjectModification:
2020_01_24-PM-05_40_33
Theory : monads
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