### Nuprl Lemma : bag-cases

`∀[T:Type]. ∀bs:bag(T). ((bs = {} ∈ bag(T)) ∨ (↓∃x:T. ∃bs':bag(T). (bs = ({x} + bs') ∈ bag(T))))`

Proof

Definitions occuring in Statement :  bag-append: `as + bs` single-bag: `{x}` empty-bag: `{}` bag: `bag(T)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` squash: `↓T` or: `P ∨ Q` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` nat: `ℕ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` guard: `{T}` squash: `↓T` exists: `∃x:A. B[x]` bag-size: `#(bs)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` false: `False` cons: `[a / b]` single-bag: `{x}` bag-append: `as + bs` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]`
Lemmas referenced :  decidable__le bag-size_wf nat_wf bag-size-zero empty-bag_wf squash_wf exists_wf bag_wf equal_wf bag-append_wf single-bag_wf bag_to_squash_list not_wf le_wf list-cases length_of_nil_lemma satisfiable-full-omega-tt intformnot_wf intformle_wf itermConstant_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_formula_prop_wf product_subtype_list length_of_cons_lemma list-subtype-bag list_ind_cons_lemma list_ind_nil_lemma cons_wf equal-wf-T-base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin isectElimination cumulativity hypothesisEquality hypothesis applyEquality lambdaEquality setElimination rename sqequalRule natural_numberEquality unionElimination inlFormation independent_isectElimination inrFormation imageElimination productElimination promote_hyp equalitySymmetry hyp_replacement Error :applyLambdaEquality,  because_Cache dependent_pairFormation intEquality isect_memberEquality voidElimination voidEquality computeAll hypothesis_subsumption imageMemberEquality baseClosed universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}bs:bag(T).  ((bs  =  \{\})  \mvee{}  (\mdownarrow{}\mexists{}x:T.  \mexists{}bs':bag(T).  (bs  =  (\{x\}  +  bs'))))

Date html generated: 2016_10_25-AM-10_22_26
Last ObjectModification: 2016_07_12-AM-06_39_07

Theory : bags

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