### Nuprl Lemma : absval_unfold

`∀[x:ℤ]. (|x| ~ if (-1) < (x)  then x  else (-x))`

Proof

Definitions occuring in Statement :  absval: `|i|` uall: `∀[x:A]. B[x]` less: `if (a) < (b)  then c  else d` minus: `-n` natural_number: `\$n` int: `ℤ` sqequal: `s ~ t`
Definitions unfolded in proof :  absval: `|i|` uall: `∀[x:A]. B[x]` member: `t ∈ T` has-value: `(a)↓` uimplies: `b supposing a` sq_type: `SQType(T)` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` 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` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` subtype_rel: `A ⊆r B` le: `A ≤ B` decidable: `Dec(P)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtract: `n - m`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  introduction cut callbyvalueReduce extract_by_obid sqequalHypSubstitution isectElimination thin intEquality independent_isectElimination hypothesis hypothesisEquality instantiate cumulativity dependent_functionElimination equalityTransitivity equalitySymmetry independent_functionElimination axiomSqEquality Error :universeIsType,  natural_numberEquality lambdaFormation unionElimination equalityElimination productElimination lessCases Error :inhabitedIsType,  isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination minusEquality because_Cache dependent_pairFormation promote_hyp addEquality applyEquality lambdaEquality

Latex:
\mforall{}[x:\mBbbZ{}].  (|x|  \msim{}  if  (-1)  <  (x)    then  x    else  (-x))

Date html generated: 2019_06_20-AM-11_24_18
Last ObjectModification: 2018_09_26-AM-10_58_21

Theory : arithmetic

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