### Nuprl Lemma : imax-list-unique

`∀[L:ℤ List]. ∀[a:ℤ].  uiff(imax-list(L) = a ∈ ℤ;(∀b∈L.b ≤ a)) supposing (a ∈ L)`

Proof

Definitions occuring in Statement :  imax-list: `imax-list(L)` l_all: `(∀x∈L.P[x])` l_member: `(x ∈ l)` list: `T List` uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` or: `P ∨ Q` not: `¬A` implies: `P `` Q` false: `False` cons: `[a / b]` top: `Top` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` prop: `ℙ` guard: `{T}` decidable: `Dec(P)` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` l_all: `(∀x∈L.P[x])` le: `A ≤ B` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k`
Lemmas referenced :  imax-list-lb list-cases length_of_nil_lemma null_nil_lemma btrue_wf member-implies-null-eq-bfalse nil_wf btrue_neq_bfalse product_subtype_list length_of_cons_lemma add_nat_plus length_wf_nat less_than_wf nat_plus_wf nat_plus_properties decidable__lt add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermConstant_wf itermVar_wf itermAdd_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_wf false_wf equal_wf imax-list-ub decidable__le intformle_wf int_formula_prop_le_lemma less_than'_wf int_seg_wf length_wf equal-wf-base int_subtype_base l_all_wf le_wf l_member_wf select_wf int_seg_properties list_subtype_base list_wf l_exists_iff le_weakening decidable__equal_int
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality intEquality dependent_functionElimination unionElimination sqequalRule independent_isectElimination equalityTransitivity equalitySymmetry independent_functionElimination voidElimination promote_hyp hypothesis_subsumption productElimination isect_memberEquality voidEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed lambdaFormation applyLambdaEquality setElimination rename pointwiseFunctionality baseApply closedConclusion dependent_pairFormation lambdaEquality int_eqEquality computeAll independent_pairEquality because_Cache axiomEquality applyEquality setEquality imageElimination productEquality

Latex:
\mforall{}[L:\mBbbZ{}  List].  \mforall{}[a:\mBbbZ{}].    uiff(imax-list(L)  =  a;(\mforall{}b\mmember{}L.b  \mleq{}  a))  supposing  (a  \mmember{}  L)

Date html generated: 2017_04_14-AM-09_23_57
Last ObjectModification: 2017_02_27-PM-03_58_52

Theory : list_1

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