### Nuprl Lemma : absval-as-imax

`∀[a:ℤ]. (imax(a;-a) = |a| ∈ ℤ)`

Proof

Definitions occuring in Statement :  imax: `imax(a;b)` absval: `|i|` uall: `∀[x:A]. B[x]` minus: `-n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` le: `A ≤ B` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_int_wf assert_of_le_int decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermMinus_wf itermVar_wf intformless_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_minus_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf le_wf squash_wf true_wf imax_unfold absval_unfold iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut hypothesis intEquality hypothesisEquality minusEquality introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache sqequalRule lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity lambdaEquality int_eqEquality computeAll applyEquality universeEquality

Latex:
\mforall{}[a:\mBbbZ{}].  (imax(a;-a)  =  |a|)

Date html generated: 2017_04_14-AM-09_13_22
Last ObjectModification: 2017_02_27-PM-03_51_01

Theory : int_2

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