Nuprl Lemma : simple-swap2_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[i,j:ℕn]. (simple-swap2(array-model(AType);i;j) ∈ A-map Unit)
Proof
Definitions occuring in Statement :
simple-swap2: simple-swap2(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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
simple-swap2: simple-swap2(AModel;i;j),
array-model: array-model(AType),
A-bind: A-bind(AModel),
A-fetch: A-fetch(AModel),
A-map: A-map,
pi2: snd(t),
pi1: fst(t),
M-map: M-map(mnd),
array-monad: array-monad(AType),
M-bind: M-bind(Mnd),
M-return: M-return(Mnd),
A-coerce: A-coerce(AModel),
let: let,
Arr: Arr(AType),
mk_monad: mk_monad(M;return;bind),
idx: idx(AType),
upd: upd(AType),
A-assign: A-assign(AModel),
A-fetch': A-fetch'(AModel),
array: array{i:l}(Val;n),
nat: ℕ
Lemmas referenced :
it_wf,
int_seg_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
lambdaEquality,
independent_pairEquality,
lemma_by_obid,
hypothesis,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination,
natural_numberEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
intEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)]. \mforall{}[i,j:\mBbbN{}n]. (simple-swap2(array-model(AType);i;j) \mmember{} A-map Unit)
Date html generated:
2016_05_15-PM-02_20_33
Last ObjectModification:
2015_12_27-AM-08_58_06
Theory : monads
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