Nuprl Lemma : map_wf_bag
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[bs:bag(A)]. (map(f;bs) ∈ bag(B))
Proof
Definitions occuring in Statement :
bag: bag(T),
map: map(f;as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
bag-map: bag-map(f;bs),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
bag-map_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[bs:bag(A)]. (map(f;bs) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-07_44_33
Last ObjectModification:
2015_12_27-AM-11_11_15
Theory : general
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