Nuprl Lemma : alt-swap-spec_wf2
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[prog:ℕn ⟶ ℕn ⟶ (A-map Unit)]. ∀[i,j:ℕn]. (alt-swap-spec(AType;n;prog) ∈ ℙ)
Proof
Definitions occuring in Statement :
alt-swap-spec: alt-swap-spec(AType;n;prog),
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],
prop: ℙ,
unit: Unit,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
alt-swap-spec: alt-swap-spec(AType;n;prog),
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
int_seg: {i..j-},
so_apply: x[s]
Lemmas referenced :
all_wf,
Arr_wf,
int_seg_wf,
equal_wf,
A-post-val_wf,
A-pre-val_wf,
not_wf,
A-map_wf,
unit_wf2,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
productEquality,
applyEquality,
functionExtensionality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)]. \mforall{}[prog:\mBbbN{}n {}\mrightarrow{} \mBbbN{}n {}\mrightarrow{} (A-map Unit)]. \mforall{}[i,j:\mBbbN{}n].
(alt-swap-spec(AType;n;prog) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_44_36
Last ObjectModification:
2017_07_26-PM-04_30_16
Theory : monads
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