Nuprl Lemma : sv-bag-only-map

[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] so_apply: x[s] 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 squash: T prop: so_lambda: λ2x.t[x] uimplies: supposing a subtype_rel: A ⊆B top: Top so_apply: x[s] implies:  Q sq_stable: SqStable(P) exists: x:A. B[x] bag-size: #(bs) sv-bag-only: sv-bag-only(b) bag-map: bag-map(f;bs) nat: listp: List+ ge: i ≥  all: x:A. B[x] decidable: Dec(P) or: P ∨ Q less_than: a < b and: P ∧ Q satisfiable_int_formula: satisfiable_int_formula(fmla) false: False not: ¬A true: True guard: {T} iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  bag_to_squash_list sq_stable__uall single-valued-bag_wf isect_wf less_than_wf bag-size_wf equal_wf sv-bag-only_wf bag-map_wf single-valued-bag-map bag-size-map sq_stable__equal squash_wf list-subtype-bag nat_wf bag_wf length_wf hd_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf hd_map iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality imageElimination cumulativity hypothesis sqequalRule lambdaEquality natural_numberEquality applyEquality because_Cache functionExtensionality independent_isectElimination isect_memberEquality voidElimination voidEquality independent_functionElimination dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry productElimination promote_hyp rename setElimination hyp_replacement applyLambdaEquality imageMemberEquality baseClosed functionEquality universeEquality dependent_set_memberEquality unionElimination dependent_pairFormation int_eqEquality intEquality independent_pairFormation computeAll

\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: 2017_10_01-AM-08_56_04
Last ObjectModification: 2017_07_26-PM-04_38_06

Theory : bags

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