Nuprl Lemma : bm_T-wf2
∀[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) supposing cnt = (1 + bm_numItems(left) + bm_numItems(right)) ∈ ℤ
Proof
Definitions occuring in Statement :
bm_numItems: bm_numItems(m),
binary-map: binary-map(T;Key),
bm_T: bm_T(key;value;cnt;left;right),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
binary-map: binary-map(T;Key),
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
prop: ℙ
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)
supposing cnt = (1 + bm\_numItems(left) + bm\_numItems(right))
Date html generated:
2016_05_17-PM-01_38_56
Last ObjectModification:
2015_12_28-PM-08_10_03
Theory : binary-map
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