Nuprl Lemma : absval_unfold2
∀[x:ℤ]. (|x| ~ if (0) < (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
Lemmas referenced :
value-type-has-value,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
sqequalAxiom
Latex:
\mforall{}[x:\mBbbZ{}]. (|x| \msim{} if (0) < (x) then x else (-x))
Date html generated:
2016_05_13-PM-03_33_38
Last ObjectModification:
2015_12_26-AM-09_44_27
Theory : arithmetic
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