Nuprl Lemma : collect_accum_wf
∀[A,B:Type]. ∀[P:B ⟶ 𝔹]. ∀[num:A ⟶ ℕ]. ∀[init:B]. ∀[f:B ⟶ A ⟶ B].
(collect_accum(x.num[x];init;a,v.f[a;v];a.P[a]) ∈ (ℤ × B × (B + Top)) ⟶ A ⟶ (ℤ × B × (B + Top)))
Proof
Definitions occuring in Statement :
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
so_apply: x[s],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
has-value: (a)↓,
nat: ℕ,
so_lambda: λ2x.t[x],
spreadn: spread3,
subtype_rel: A ⊆r B,
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Latex:
\mforall{}[A,B:Type]. \mforall{}[P:B {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[init:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(collect\_accum(x.num[x];init;a,v.f[a;v];a.P[a]) \mmember{} (\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)) {}\mrightarrow{} A {}\mrightarrow{} (\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)))
Date html generated:
2016_05_16-AM-10_11_40
Last ObjectModification:
2015_12_28-PM-09_25_32
Theory : new!event-ordering
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