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
Home
Index