Nuprl Lemma : sv-bag-only-append

[A:Type]. ∀[as,bs:bag(A)].
  (sv-bag-only(as bs) sv-bag-only(as) ∈ A) supposing 
     (similar-bags(A;as;bs) and 
     0 < #(as) and 
     single-valued-bag(as;A) and 


Definitions occuring in Statement :  sv-bag-only: sv-bag-only(b) single-valued-bag: single-valued-bag(b;T) similar-bags: similar-bags(A;as;bs) bag-size: #(bs) bag-append: as bs bag: bag(T) less_than: a < b uimplies: supposing a uall: [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 squash: T exists: x:A. B[x] implies:  Q prop: subtype_rel: A ⊆B nat: true: True and: P ∧ Q cand: c∧ B top: Top all: x:A. B[x] decidable: Dec(P) or: P ∨ Q guard: {T} ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) false: False not: ¬A sv-bag-only: sv-bag-only(b) bag-append: as bs bag-size: #(bs) listp: List+ iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  bag_to_squash_list similar-bags_wf less_than_wf bag-size_wf single-valued-bag_wf bag_wf nat_wf single-valued-bag-append bag-size-append decidable__lt nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformnot_wf intformless_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_add_lemma int_formula_prop_wf hd-append-sq subtype_rel_list top_wf length_wf hd_wf listp_properties list-subtype-bag squash_wf true_wf equal_wf sv-bag-only_wf bag-append_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality imageElimination productElimination independent_functionElimination hypothesis cumulativity sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry natural_numberEquality applyEquality lambdaEquality setElimination rename universeEquality independent_isectElimination independent_pairFormation voidElimination voidEquality dependent_functionElimination addEquality unionElimination applyLambdaEquality dependent_pairFormation int_eqEquality intEquality computeAll lambdaFormation dependent_set_memberEquality functionEquality imageMemberEquality baseClosed productEquality

\mforall{}[A:Type].  \mforall{}[as,bs:bag(A)].
    (sv-bag-only(as  +  bs)  =  sv-bag-only(as))  supposing 
          (similar-bags(A;as;bs)  and 
          0  <  \#(as)  and 
          single-valued-bag(as;A)  and 

Date html generated: 2017_10_01-AM-08_55_52
Last ObjectModification: 2017_07_26-PM-04_37_57

Theory : bags

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