Nuprl Lemma : sub-bag_antisymmetry

[T:Type]. ∀[as,bs:bag(T)].  (as bs ∈ bag(T)) supposing (sub-bag(T;as;bs) and sub-bag(T;bs;as))


Definitions occuring in Statement :  sub-bag: sub-bag(T;as;bs) bag: bag(T) uimplies: supposing a uall: [x:A]. B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  sub-bag: sub-bag(T;as;bs) uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a exists: x:A. B[x] subtype_rel: A ⊆B nat: top: Top prop: so_lambda: λ2x.t[x] so_apply: x[s] empty-bag: {} all: x:A. B[x] decidable: Dec(P) or: P ∨ Q guard: {T} ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) false: False implies:  Q not: ¬A and: P ∧ Q
Lemmas referenced :  bag-subtype-list bag-append-empty int_formula_prop_wf int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma itermAdd_wf intformeq_wf intformnot_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt le_wf nat_properties decidable__le bag-size-zero bag-append_wf equal_wf bag_wf exists_wf bag-size-append nat_wf bag-size_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin hypothesis applyEquality lambdaEquality lemma_by_obid isectElimination hypothesisEquality setElimination rename because_Cache isect_memberEquality voidElimination voidEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality independent_isectElimination dependent_functionElimination unionElimination setEquality intEquality natural_numberEquality dependent_pairFormation int_eqEquality independent_pairFormation computeAll

\mforall{}[T:Type].  \mforall{}[as,bs:bag(T)].    (as  =  bs)  supposing  (sub-bag(T;as;bs)  and  sub-bag(T;bs;as))

Date html generated: 2016_05_15-PM-02_35_51
Last ObjectModification: 2016_01_16-AM-08_52_13

Theory : bags

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