### Nuprl Lemma : absval_neg

`∀[i:{...0}]. (|i| = (-i) ∈ ℤ)`

Proof

Definitions occuring in Statement :  absval: `|i|` int_lower: `{...i}` uall: `∀[x:A]. B[x]` minus: `-n` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` int_lower: `{...i}` 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` decidable: `Dec(P)` subtype_rel: `A ⊆r B` subtract: `n - m`
Lemmas referenced :  absval_unfold lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int 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 int_lower_wf int_lower_properties int_subtype_base decidable__int_equal false_wf not-equal-2 less-iff-le add_functionality_wrt_le add-associates add-swap add-zero le-add-cancel condition-implies-le add-commutes minus-add minus-zero
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut sqequalRule introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis minusEquality natural_numberEquality because_Cache lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate impliesFunctionality cumulativity intEquality addEquality applyEquality lambdaEquality

Latex:
\mforall{}[i:\{...0\}].  (|i|  =  (-i))

Date html generated: 2017_04_14-AM-07_16_49
Last ObjectModification: 2017_02_27-PM-02_51_38

Theory : arithmetic

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