Nuprl Lemma : bm_cnt_prop_T
∀[T,Key:Type]. ∀[key:Key]. ∀[value:T]. ∀[cnt:ℤ]. ∀[left,right:binary_map(T;Key)].
uiff(↑bm_cnt_prop(bm_T(key;value;cnt;left;right));(cnt = (1 + bm_numItems(left) + bm_numItems(right)) ∈ ℤ)
∧ (↑bm_cnt_prop(left))
∧ (↑bm_cnt_prop(right)))
Proof
Definitions occuring in Statement :
bm_numItems: bm_numItems(m),
bm_cnt_prop: bm_cnt_prop(m),
bm_T: bm_T(key;value;cnt;left;right),
binary_map: binary_map(T;Key),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bm_cnt_prop: bm_cnt_prop(m),
top: Top,
pi2: snd(t),
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Latex:
\mforall{}[T,Key:Type]. \mforall{}[key:Key]. \mforall{}[value:T]. \mforall{}[cnt:\mBbbZ{}]. \mforall{}[left,right:binary\_map(T;Key)].
uiff(\muparrow{}bm\_cnt\_prop(bm\_T(key;value;cnt;left;right));(cnt
= (1 + bm\_numItems(left) + bm\_numItems(right)))
\mwedge{} (\muparrow{}bm\_cnt\_prop(left))
\mwedge{} (\muparrow{}bm\_cnt\_prop(right)))
Date html generated:
2016_05_17-PM-01_38_50
Last ObjectModification:
2015_12_28-PM-08_10_57
Theory : binary-map
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