Nuprl Lemma : select-tagged-indices-aux_wf
∀[A,B:Type]. ∀[tg:A ⟶ B]. ∀[P:A ⟶ 𝔹]. ∀[L:A List]. (select-tagged-indices-aux(P;tg;L) ∈ ℕ ⟶ ((ℕ × B) List))
Proof
Definitions occuring in Statement :
select-tagged-indices-aux: select-tagged-indices-aux(P;tg;L),
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
select-tagged-indices-aux: select-tagged-indices-aux(P;tg;L),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
bool: 𝔹,
unit: Unit,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[A,B:Type]. \mforall{}[tg:A {}\mrightarrow{} B]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[L:A List].
(select-tagged-indices-aux(P;tg;L) \mmember{} \mBbbN{} {}\mrightarrow{} ((\mBbbN{} \mtimes{} B) List))
Date html generated:
2016_05_17-AM-11_31_16
Last ObjectModification:
2016_01_18-AM-07_47_19
Theory : event-logic-applications
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