Nuprl Lemma : bm_T_wf
∀[T,Key:Type]. ∀[key:Key]. ∀[value:T]. ∀[cnt:ℤ]. ∀[left,right:binary_map(T;Key)].
(bm_T(key;value;cnt;left;right) ∈ binary_map(T;Key))
Proof
Definitions occuring in Statement :
bm_T: bm_T(key;value;cnt;left;right),
binary_map: binary_map(T;Key),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
binary_map: binary_map(T;Key),
bm_T: bm_T(key;value;cnt;left;right),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
binary_mapco_size: binary_mapco_size(p),
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
binary_map_size: binary_map_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[T,Key:Type]. \mforall{}[key:Key]. \mforall{}[value:T]. \mforall{}[cnt:\mBbbZ{}]. \mforall{}[left,right:binary\_map(T;Key)].
(bm\_T(key;value;cnt;left;right) \mmember{} binary\_map(T;Key))
Date html generated:
2016_05_17-PM-01_37_13
Last ObjectModification:
2015_12_28-PM-08_11_18
Theory : binary-map
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