Nuprl Lemma : bag-combine-empty-right

[T:Type]. ∀[bs:bag(T)].  (⋃x∈bs.{} {})


Proof




Definitions occuring in Statement :  bag-combine: x∈bs.f[x] empty-bag: {} bag: bag(T) uall: [x:A]. B[x] universe: Type sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T subtype_rel: A ⊆B all: x:A. B[x] implies:  Q prop: empty-bag: {} bag-combine: x∈bs.f[x] bag-map: bag-map(f;bs) bag-union: bag-union(bbs) concat: concat(ll) nat: false: False ge: i ≥  uimplies: 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: λ2y.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_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{}[T:Type].  \mforall{}[bs:bag(T)].    (\mcup{}x\mmember{}bs.\{\}  \msim{}  \{\})



Date html generated: 2017_10_01-AM-08_47_12
Last ObjectModification: 2017_07_26-PM-04_31_48

Theory : bags


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