Nuprl Lemma : collect_accum-wf2
∀[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]) ∈ {s:ℤ × B × (B + Top)| (↑isl(snd(snd(s)))) ⇒ (1 ≤ (fst(s)))}
⟶ A
⟶ {s:ℤ × B × (B + Top)| (↑isl(snd(snd(s)))) ⇒ (1 ≤ (fst(s)))} )
Proof
Definitions occuring in Statement :
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
nat: ℕ,
assert: ↑b,
isl: isl(x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
le: A ≤ B,
implies: P ⇒ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
natural_number: $n,
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]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
has-value: (a)↓,
nat: ℕ,
spreadn: spread3,
pi2: snd(t),
pi1: fst(t),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
isl: isl(x),
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_apply: x[s1;s2],
decidable: Dec(P),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
isr: isr(x)
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{} \{s:\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)|
(\muparrow{}isl(snd(snd(s)))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} A
{}\mrightarrow{} \{s:\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)| (\muparrow{}isl(snd(snd(s)))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\} )
Date html generated:
2016_05_16-AM-10_12_21
Last ObjectModification:
2016_01_17-PM-01_22_26
Theory : new!event-ordering
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