### Nuprl Lemma : absval-minus

`∀[x:ℤ]. (|-x| = |x| ∈ ℤ)`

Proof

Definitions occuring in Statement :  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` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` le: `A ≤ B`
Lemmas referenced :  absval_unfold2 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 iff_transitivity assert_wf bnot_wf not_wf iff_weakening_uiff assert_of_bnot minus-minus add_functionality_wrt_lt le_reflexive less_than_transitivity2 le_weakening2 less_than_irreflexivity minus-one-mul zero-add add-commutes add-mul-special zero-mul not-lt-2 int_subtype_base minus-zero add_functionality_wrt_le le_antisymmetry
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut sqequalRule introduction extract_by_obid sqequalHypSubstitution isectElimination thin minusEquality hypothesisEquality hypothesis natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate impliesFunctionality cumulativity multiplyEquality intEquality

Latex:
\mforall{}[x:\mBbbZ{}].  (|-x|  =  |x|)

Date html generated: 2017_04_14-AM-07_16_54
Last ObjectModification: 2017_02_27-PM-02_51_41

Theory : arithmetic

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