Nuprl Lemma : bm_collate_next_wf
∀[T,Key:Type]. ∀[l:binary-map(T;Key) List]. (bm_collate_next(l) ∈ binary-map(T;Key) × (binary-map(T;Key) List))
Proof
Definitions occuring in Statement :
bm_collate_next: bm_collate_next(l),
binary-map: binary-map(T;Key),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bm_collate_next: bm_collate_next(l),
all: ∀x:A. B[x],
or: P ∨ Q,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
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_E: bm_E(),
btrue: tt,
true: True,
binary-map: binary-map(T;Key),
prop: ℙ,
cons: [a / b],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5]
Latex:
\mforall{}[T,Key:Type]. \mforall{}[l:binary-map(T;Key) List].
(bm\_collate\_next(l) \mmember{} binary-map(T;Key) \mtimes{} (binary-map(T;Key) List))
Date html generated:
2016_05_17-PM-01_43_09
Last ObjectModification:
2015_12_28-PM-08_08_40
Theory : binary-map
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