Nuprl Lemma : sv-bag-only-map2

[A,B:Type]. ∀[f:A ⟶ B]. ∀[b:bag(A)].
  (sv-bag-only(bag-map(f;b)) (f sv-bag-only(b)) ∈ B) supposing (0 < #(b) and single-valued-bag(b;A))


Definitions occuring in Statement :  sv-bag-only: sv-bag-only(b) single-valued-bag: single-valued-bag(b;T) bag-size: #(bs) bag-map: bag-map(f;bs) bag: bag(T) less_than: a < b uimplies: supposing a uall: [x:A]. B[x] apply: a function: x:A ⟶ B[x] natural_number: $n universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a so_apply: x[s] prop: subtype_rel: A ⊆B nat:
Lemmas referenced :  sv-bag-only-map less_than_wf bag-size_wf nat_wf single-valued-bag_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis natural_numberEquality applyEquality lambdaEquality setElimination rename sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry functionEquality universeEquality

\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].  \mforall{}[b:bag(A)].
    (sv-bag-only(bag-map(f;b))  =  (f  sv-bag-only(b)))  supposing  (0  <  \#(b)  and  single-valued-bag(b;A))

Date html generated: 2016_05_15-PM-02_44_09
Last ObjectModification: 2015_12_27-AM-09_38_33

Theory : bags

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