Nuprl Lemma : simple-swap3_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[i,j:ℕn]. (simple-swap3(array-model(AType);i;j) ∈ A-map Unit)
Proof
Definitions occuring in Statement :
simple-swap3: simple-swap3(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-swap3: simple-swap3(AModel;i;j),
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ
Lemmas referenced :
A-bind2_wf,
unit_wf2,
A-fetch2_wf,
A-assign2_wf,
int_seg_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)]. \mforall{}[i,j:\mBbbN{}n]. (simple-swap3(array-model(AType);i;j) \mmember{} A-map Unit)
Date html generated:
2016_05_15-PM-02_20_47
Last ObjectModification:
2015_12_27-AM-08_57_56
Theory : monads
Home
Index