Nuprl Lemma : collect_filter_accum_fun_wf
∀[A,B:Type]. ∀[base:B]. ∀[f:B ⟶ A ⟶ B]. ∀[size:ℕ+]. ∀[num:A ⟶ ℕ]. ∀[P:A ⟶ 𝔹].
(collect_filter_accum_fun(b,v.f[b;v];base;size;v.num[v];v.P[v]) ∈ {s:ℤ × ℕ × B × (𝔹 + Top)|
(↑isl(snd(snd(snd(s))))) ⇒ (1 ≤ (fst(s)))}
⟶ A
⟶ {s:ℤ × ℕ × B × (𝔹 + Top)| (↑isl(snd(snd(snd(s))))) ⇒ (1 ≤ (fst(s)))} )
Proof
Definitions occuring in Statement :
collect_filter_accum_fun: collect_filter_accum_fun(b,v.f[b; v];base;size;v.num[v];v.P[v]),
nat_plus: ℕ+,
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_filter_accum_fun: collect_filter_accum_fun(b,v.f[b; v];base;size;v.num[v];v.P[v]),
spreadn: spread4,
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
prop: ℙ,
isl: isl(x),
not: ¬A,
false: False,
top: Top,
pi1: fst(t),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nat_plus: ℕ+,
le: A ≤ B,
less_than': less_than'(a;b),
so_apply: x[s1;s2],
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
nequal: a ≠ b ∈ T
Latex:
\mforall{}[A,B:Type]. \mforall{}[base:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
(collect\_filter\_accum\_fun(b,v.f[b;v];base;size;v.num[v];v.P[v]) \mmember{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)|
(\muparrow{}isl(snd(snd(snd(s)))))
{}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} A
{}\mrightarrow{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)| (\muparrow{}isl(snd(snd(snd(s))))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\} )
Date html generated:
2016_05_16-AM-10_12_39
Last ObjectModification:
2016_01_17-PM-01_33_31
Theory : new!event-ordering
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