### Nuprl Lemma : bag-combine-unit-right

`∀[A:Type]. ∀[bs:bag(A)].  (⋃x∈bs.[x] ~ bs)`

Proof

Definitions occuring in Statement :  bag-combine: `⋃x∈bs.f[x]` bag: `bag(T)` cons: `[a / b]` nil: `[]` uall: `∀[x:A]. B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` Q` prop: `ℙ` bag-combine: `⋃x∈bs.f[x]` bag-map: `bag-map(f;bs)` bag-union: `bag-union(bbs)` concat: `concat(ll)` nat: `ℕ` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` guard: `{T}` or: `P ∨ Q` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` nil: `[]` it: `⋅` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]`
Lemmas referenced :  bag-subtype-list list_wf top_wf equal_wf bag_wf nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_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 ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases map_nil_lemma reduce_nil_lemma product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int map_cons_lemma reduce_cons_lemma list_ind_cons_lemma list_ind_nil_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesisEquality applyEquality extract_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesis sqequalRule isectElimination lambdaFormation equalityTransitivity equalitySymmetry independent_functionElimination sqequalAxiom cumulativity isect_memberEquality because_Cache universeEquality setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll unionElimination promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate imageElimination

Latex:
\mforall{}[A:Type].  \mforall{}[bs:bag(A)].    (\mcup{}x\mmember{}bs.[x]  \msim{}  bs)

Date html generated: 2017_10_01-AM-08_47_15
Last ObjectModification: 2017_07_26-PM-04_31_50

Theory : bags

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