Nuprl Lemma : bm_T'_wf
∀[T,Key:Type]. ∀[k:Key]. ∀[v:T]. ∀[m1,m2:binary-map(T;Key)]. (bm_T'(k;v;m1;m2) ∈ binary-map(T;Key))
Proof
Definitions occuring in Statement :
bm_T': bm_T'(k;v;m1;m2),
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,
binary-map: binary-map(T;Key),
bm_T': bm_T'(k;v;m1;m2),
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),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bm_E: bm_E(),
assert: ↑b,
top: Top,
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
binary_map: binary_map(T;Key),
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),
true: True,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
false: False,
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
bm_T?: bm_T?(v),
bm_T-left: bm_T-left(v),
bm_T-right: bm_T-right(v),
le: A ≤ B,
bm_wt: bm_wt(i)
Latex:
\mforall{}[T,Key:Type]. \mforall{}[k:Key]. \mforall{}[v:T]. \mforall{}[m1,m2:binary-map(T;Key)]. (bm\_T'(k;v;m1;m2) \mmember{} binary-map(T;Key))
Date html generated:
2016_05_17-PM-01_40_09
Last ObjectModification:
2016_01_17-AM-11_21_26
Theory : binary-map
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