Nuprl Lemma : simple-swap-specification_wf
∀[n:ℕ]. ∀[AType:array{i:l}(ℤ;n)]. ∀[prog:A-map Unit]. ∀i,j:ℕn. (simple-swap-specification(AType;n;prog;i;j) ∈ ℙ)
Proof
Definitions occuring in Statement :
simple-swap-specification: simple-swap-specification(AType;n;prog;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],
prop: ℙ,
all: ∀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,
all: ∀x:A. B[x],
simple-swap-specification: simple-swap-specification(AType;n;prog;i;j),
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
Arr_wf,
assert_wf,
A-eval_wf,
bool_wf,
A-map_wf,
simple-swap-test2_wf,
unit_wf2,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
intEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
dependent_functionElimination,
axiomEquality,
because_Cache,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(\mBbbZ{};n)]. \mforall{}[prog:A-map Unit].
\mforall{}i,j:\mBbbN{}n. (simple-swap-specification(AType;n;prog;i;j) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-02_20_07
Last ObjectModification:
2015_12_27-AM-08_58_02
Theory : monads
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