Nuprl Lemma : bm_N_wf
∀[T,Key:Type]. ∀[k:Key]. ∀[v:T]. ∀[m1,m2:binary-map(T;Key)]. (bm_N(k;v;m1;m2) ∈ binary-map(T;Key))
Proof
Definitions occuring in Statement :
bm_N: bm_N(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_N: bm_N(k;v;m1;m2),
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
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,
binary_map: binary_map(T;Key),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
false: False,
bm_T: bm_T(key;value;cnt;left;right),
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
true: True
Latex:
\mforall{}[T,Key:Type]. \mforall{}[k:Key]. \mforall{}[v:T]. \mforall{}[m1,m2:binary-map(T;Key)]. (bm\_N(k;v;m1;m2) \mmember{} binary-map(T;Key))
Date html generated:
2016_05_17-PM-01_39_36
Last ObjectModification:
2016_01_17-AM-11_20_27
Theory : binary-map
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