Nuprl Lemma : bm_double_L_wf
∀[T,Key:Type]. ∀[a:Key]. ∀[av:T]. ∀[w,m:binary-map(T;Key)].
(bm_double_L(a;av;w;m) ∈ binary-map(T;Key)) supposing ((↑bm_T?(bm_T-left(m))) and (↑bm_T?(m)))
Proof
Definitions occuring in Statement :
bm_double_L: bm_double_L(a;av;w;m),
binary-map: binary-map(T;Key),
bm_T-left: bm_T-left(v),
bm_T?: bm_T?(v),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
binary-map: binary-map(T;Key),
bm_double_L: bm_double_L(a;av;w;m),
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(),
bm_T-left: bm_T-left(v),
pi2: snd(t),
bm_T?: bm_T?(v),
pi1: fst(t),
assert: ↑b,
bfalse: ff,
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
top: Top,
so_apply: x[s1;s2;s3;s4;s5],
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
bm_T: bm_T(key;value;cnt;left;right)
Latex:
\mforall{}[T,Key:Type]. \mforall{}[a:Key]. \mforall{}[av:T]. \mforall{}[w,m:binary-map(T;Key)].
(bm\_double\_L(a;av;w;m) \mmember{} binary-map(T;Key)) supposing ((\muparrow{}bm\_T?(bm\_T-left(m))) and (\muparrow{}bm\_T?(m)))
Date html generated:
2016_05_17-PM-01_39_52
Last ObjectModification:
2015_12_28-PM-08_10_23
Theory : binary-map
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