Nuprl Lemma : bm_singleton_wf
∀[T,Key:Type]. ∀[x:Key]. ∀[v:T]. (bm_singleton(x;v) ∈ binary-map(T;Key))
Proof
Definitions occuring in Statement :
bm_singleton: bm_singleton(x;v),
binary-map: binary-map(T;Key),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bm_singleton: bm_singleton(x;v),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bm_cnt_prop: bm_cnt_prop(m),
pi2: snd(t),
bm_cnt_prop0: bm_cnt_prop0(m),
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
bm_T: bm_T(key;value;cnt;left;right),
band: p ∧b q,
eq_int: (i =z j),
pi1: fst(t),
bm_E: bm_E(),
btrue: tt,
true: True,
binary-map: binary-map(T;Key),
prop: ℙ
Latex:
\mforall{}[T,Key:Type]. \mforall{}[x:Key]. \mforall{}[v:T]. (bm\_singleton(x;v) \mmember{} binary-map(T;Key))
Date html generated:
2016_05_17-PM-01_40_29
Last ObjectModification:
2015_12_28-PM-08_09_37
Theory : binary-map
Home
Index