### Nuprl Lemma : imax-bag-ub

`∀[bs:bag(ℤ)]. ∀[x:ℤ].  (x ↓∈ bs `` (x ≤ imax-bag(bs)))`

Proof

Definitions occuring in Statement :  bag-member: `x ↓∈ bs` imax-bag: `imax-bag(bs)` bag: `bag(T)` uall: `∀[x:A]. B[x]` le: `A ≤ B` implies: `P `` Q` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` squash: `↓T` prop: `ℙ` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` exists: `∃x:A. B[x]` so_apply: `x[s]` all: `∀x:A. B[x]` sq_stable: `SqStable(P)` le: `A ≤ B` not: `¬A` false: `False` imax-bag: `imax-bag(bs)` bag-size: `#(bs)` subtype_rel: `A ⊆r B` cand: `A c∧ B` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  bag_to_squash_list sq_stable__all bag-member_wf le_wf imax-bag_wf bag-size-bag-member sq_stable__le less_than'_wf squash_wf imax-list-ub bag_wf list-subtype-bag subtype_rel_self l_exists_iff l_member_wf bag-member-list decidable__int_equal decidable__le satisfiable-full-omega-tt intformnot_wf intformle_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation thin extract_by_obid sqequalHypSubstitution isectElimination because_Cache hypothesisEquality imageElimination intEquality hypothesis sqequalRule lambdaEquality independent_isectElimination productElimination independent_functionElimination dependent_pairFormation imageMemberEquality baseClosed dependent_functionElimination independent_pairEquality voidElimination axiomEquality equalityTransitivity equalitySymmetry promote_hyp rename hyp_replacement Error :applyLambdaEquality,  functionEquality isect_memberEquality applyEquality setElimination setEquality independent_pairFormation unionElimination natural_numberEquality int_eqEquality voidEquality computeAll productEquality

Latex:
\mforall{}[bs:bag(\mBbbZ{})].  \mforall{}[x:\mBbbZ{}].    (x  \mdownarrow{}\mmember{}  bs  {}\mRightarrow{}  (x  \mleq{}  imax-bag(bs)))

Date html generated: 2016_10_25-AM-10_32_11
Last ObjectModification: 2016_07_12-AM-06_48_04

Theory : bags

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