### Nuprl Lemma : imax-list-member

`∀L:ℤ List. (imax-list(L) ∈ L) supposing 0 < ||L||`

Proof

Definitions occuring in Statement :  imax-list: `imax-list(L)` l_member: `(x ∈ l)` length: `||as||` list: `T List` less_than: `a < b` uimplies: `b supposing a` all: `∀x:A. B[x]` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  imax-list: `imax-list(L)` all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` implies: `P `` Q` prop: `ℙ` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` guard: `{T}` or: `P ∨ Q` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` subtype_rel: `A ⊆r B` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  member-less_than length_wf combine-list-member imax_wf less_than_wf list_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int decidable__equal_int satisfiable-full-omega-tt intformnot_wf intformeq_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_wf equal-wf-base int_subtype_base eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf or_wf squash_wf true_wf imax_unfold iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality intEquality hypothesisEquality hypothesis independent_isectElimination rename dependent_functionElimination lambdaEquality independent_functionElimination because_Cache unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination inrFormation dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll applyEquality promote_hyp instantiate cumulativity inlFormation imageElimination universeEquality imageMemberEquality baseClosed

Latex:
\mforall{}L:\mBbbZ{}  List.  (imax-list(L)  \mmember{}  L)  supposing  0  <  ||L||

Date html generated: 2017_04_14-AM-09_23_59
Last ObjectModification: 2017_02_27-PM-03_59_02

Theory : list_1

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