Nuprl Lemma : bm_delmin_wf
∀[T,Key:Type]. ∀[m:binary-map(T;Key)].  bm_delmin(m) ∈ binary-map(T;Key) supposing ↑bm_T?(m)
Proof
Definitions occuring in Statement : 
bm_delmin: bm_delmin(m)
, 
binary-map: binary-map(T;Key)
, 
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)
, 
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_delmin: bm_delmin(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\_delmin(m)  \mmember{}  binary-map(T;Key)  supposing  \muparrow{}bm\_T?(m)
Date html generated:
2016_05_17-PM-01_40_19
Last ObjectModification:
2016_01_17-AM-11_20_52
Theory : binary-map
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