Nuprl Lemma : binary_mapco_size_wf
∀[T,Key:Type]. ∀[p:binary_mapco(T;Key)]. (binary_mapco_size(p) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
binary_mapco_size: binary_mapco_size(p),
binary_mapco: binary_mapco(T;Key),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
binary_mapco: binary_mapco(T;Key),
eq_atom: x =a y,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
binary_mapco_size: binary_mapco_size(p)
Latex:
\mforall{}[T,Key:Type]. \mforall{}[p:binary\_mapco(T;Key)]. (binary\_mapco\_size(p) \mmember{} partial(\mBbbN{}))
Date html generated:
2016_05_17-PM-01_36_57
Last ObjectModification:
2015_12_28-PM-08_11_30
Theory : binary-map
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