Nuprl Lemma : union-nat-missing-pos_wf
∀[s1:nat-missing-type()]. ∀[max:ℕ]. ∀[missing:ℕ List]. (union-nat-missing-pos(s1;max;missing) ∈ nat-missing-type())
Proof
Definitions occuring in Statement :
union-nat-missing-pos: union-nat-missing-pos(s1;max;missing),
nat-missing-type: nat-missing-type(),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
union-nat-missing-pos: union-nat-missing-pos(s1;max;missing),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b)
Latex:
\mforall{}[s1:nat-missing-type()]. \mforall{}[max:\mBbbN{}]. \mforall{}[missing:\mBbbN{} List].
(union-nat-missing-pos(s1;max;missing) \mmember{} nat-missing-type())
Date html generated:
2016_05_17-PM-01_45_28
Last ObjectModification:
2016_01_17-AM-11_37_03
Theory : datatype-signatures
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