Nuprl Lemma : bm_numItems_is_cnt_prop0
∀[T,Key:Type]. ∀[m:binary_map(T;Key)]. (bm_numItems(m) ~ fst(bm_cnt_prop0(m)))
Proof
Definitions occuring in Statement :
bm_numItems: bm_numItems(m),
bm_cnt_prop0: bm_cnt_prop0(m),
binary_map: binary_map(T;Key),
uall: ∀[x:A]. B[x],
pi1: fst(t),
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bm_E: bm_E(),
pi1: fst(t),
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
bm_T: bm_T(key;value;cnt;left;right),
top: Top,
binary_map: binary_map(T;Key)
Latex:
\mforall{}[T,Key:Type]. \mforall{}[m:binary\_map(T;Key)]. (bm\_numItems(m) \msim{} fst(bm\_cnt\_prop0(m)))
Date html generated:
2016_05_17-PM-01_38_47
Last ObjectModification:
2015_12_28-PM-08_10_47
Theory : binary-map
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