Nuprl Lemma : bm_min_wf
∀[T,Key:Type]. ∀[m:binary_map(T;Key)]. bm_min(m) ∈ Key × T supposing ↑bm_T?(m)
Proof
Definitions occuring in Statement :
bm_min: bm_min(m),
bm_T?: bm_T?(v),
binary_map: binary_map(T;Key),
assert: ↑b,
uimplies: b supposing a,
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,
uimplies: b supposing a,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bm_E: bm_E(),
binary_map_size: binary_map_size(p),
bm_T?: bm_T?(v),
pi1: fst(t),
assert: ↑b,
bfalse: ff,
bnot: ¬bb,
bm_T: bm_T(key;value;cnt;left;right),
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
bm_min: bm_min(m),
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
true: True
Latex:
\mforall{}[T,Key:Type]. \mforall{}[m:binary\_map(T;Key)]. bm\_min(m) \mmember{} Key \mtimes{} T supposing \muparrow{}bm\_T?(m)
Date html generated:
2016_05_17-PM-01_40_14
Last ObjectModification:
2016_01_17-AM-11_21_06
Theory : binary-map
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