Nuprl Lemma : bm_unionWith_wf
∀[T,Key:Type]. ∀[compare:bm_compare(Key)]. ∀[m1,m2:binary-map(T;Key)]. ∀[f:T ⟶ T ⟶ T].
(bm_unionWith(compare;f;m1;m2) ∈ binary-map(T;Key))
Proof
Definitions occuring in Statement :
bm_unionWith: bm_unionWith(compare;f;m1;m2),
bm_compare: bm_compare(K),
binary-map: binary-map(T;Key),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bm_unionWith: bm_unionWith(compare;f;m1;m2),
binary-map: binary-map(T;Key),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T}
Latex:
\mforall{}[T,Key:Type]. \mforall{}[compare:bm\_compare(Key)]. \mforall{}[m1,m2:binary-map(T;Key)]. \mforall{}[f:T {}\mrightarrow{} T {}\mrightarrow{} T].
(bm\_unionWith(compare;f;m1;m2) \mmember{} binary-map(T;Key))
Date html generated:
2016_05_17-PM-01_43_54
Last ObjectModification:
2015_12_28-PM-08_08_38
Theory : binary-map
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