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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
threshold_accum: threshold_accum,
pi1: fst(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\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:
2016_05_16-AM-10_09_07
Last ObjectModification:
2015_12_28-PM-09_26_36
Theory : new!event-ordering
Home
Index