Nuprl Lemma : bm_remove_wf
∀[T,Key:Type]. ∀[compare:bm_compare(Key)]. ∀[x:Key]. ∀[m:binary-map(T;Key)].
bm_remove(compare;m;x) ∈ binary-map(T;Key) × T supposing ↑bm_inDomain(compare;m;x)
Proof
Definitions occuring in Statement :
bm_remove: bm_remove(compare;m;x),
bm_inDomain: bm_inDomain(compare;m;x),
bm_compare: bm_compare(K),
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,
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},
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
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_remove: bm_remove(compare;m;x),
bm_inDomain: bm_inDomain(compare;m;x),
assert: ↑b,
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
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_compare: bm_compare(K),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[T,Key:Type]. \mforall{}[compare:bm\_compare(Key)]. \mforall{}[x:Key]. \mforall{}[m:binary-map(T;Key)].
bm\_remove(compare;m;x) \mmember{} binary-map(T;Key) \mtimes{} T supposing \muparrow{}bm\_inDomain(compare;m;x)
Date html generated:
2016_05_17-PM-01_42_21
Last ObjectModification:
2016_01_17-AM-11_21_21
Theory : binary-map
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