Nuprl Lemma : threshold_accum_wf
∀[S,A,B:Type]. ∀[test:S ─→ A ─→ 𝔹]. ∀[nxt:(S × A) ─→ S]. ∀[step:S ─→ A ─→ S]. ∀[g:(S × A) ─→ (B?)].
(threshold_accum(test;
nxt;
step;
g) ∈ (S × (B?)) ─→ A ─→ (S × (B?)))
Proof
Definitions occuring in Statement :
threshold_accum: threshold_accum,
bool: 𝔹,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
universe: Type
Lemmas :
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
it_wf,
unit_wf2
\mforall{}[S,A,B:Type]. \mforall{}[test:S {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}]. \mforall{}[nxt:(S \mtimes{} A) {}\mrightarrow{} S]. \mforall{}[step:S {}\mrightarrow{} A {}\mrightarrow{} S]. \mforall{}[g:(S \mtimes{} A) {}\mrightarrow{} (B?)].
(threshold\_accum(test;
nxt;
step;
g) \mmember{} (S \mtimes{} (B?)) {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} (B?)))
Date html generated:
2015_07_17-AM-08_59_01
Last ObjectModification:
2015_01_27-PM-01_03_50
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