### Nuprl Lemma : bigger-int-property2

`∀[L:ℤ List]. ∀[n:ℤ].  (n ≤ bigger-int(n;L))`

Proof

Definitions occuring in Statement :  bigger-int: `bigger-int(n;L)` list: `T List` uall: `∀[x:A]. B[x]` le: `A ≤ B` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` guard: `{T}` le: `A ≤ B` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` subtype_rel: `A ⊆r B` less_than': `less_than'(a;b)` less_than: `a < b` squash: `↓T` bigger-int: `bigger-int(n;L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` cons: `[a / b]` assert: `↑b` ifthenelse: `if b then t else f fi ` bfalse: `ff` iff: `P `⇐⇒` Q` uiff: `uiff(P;Q)` rev_implies: `P `` Q` int_iseg: `{i...j}` cand: `A c∧ B` has-value: `(a)↓` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` sq_type: `SQType(T)` bnot: `¬bb`
Lemmas referenced :  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 less_than'_wf bigger-int_wf le_wf length_wf list_wf int_seg_wf int_seg_properties decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma decidable__equal_int int_seg_subtype false_wf intformeq_wf int_formula_prop_eq_lemma non_neg_length decidable__lt lelt_wf decidable__assert null_wf list-cases list_accum_nil_lemma nil_wf product_subtype_list null_cons_lemma last-lemma-sq pos_length iff_transitivity not_wf equal-wf-base list_subtype_base int_subtype_base assert_wf bnot_wf assert_of_null iff_weakening_uiff assert_of_bnot firstn_wf length_firstn append_wf cons_wf last_wf itermAdd_wf int_term_value_add_lemma nat_wf length_wf_nat list_accum_append subtype_rel_list top_wf equal_wf list_accum_cons_lemma value-type-has-value int-value-type le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination productElimination independent_pairEquality axiomEquality equalityTransitivity equalitySymmetry because_Cache unionElimination applyEquality applyLambdaEquality hypothesis_subsumption dependent_set_memberEquality imageElimination promote_hyp baseClosed impliesFunctionality productEquality addEquality callbyvalueReduce equalityElimination instantiate cumulativity

Latex:
\mforall{}[L:\mBbbZ{}  List].  \mforall{}[n:\mBbbZ{}].    (n  \mleq{}  bigger-int(n;L))

Date html generated: 2017_04_17-AM-07_49_00
Last ObjectModification: 2017_02_27-PM-04_22_45

Theory : list_1

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