Nuprl Lemma : rabs-as-rmax
∀[x:Top]. (|x| ~ rmax(x;-(x)))
Proof
Definitions occuring in Statement :
rabs: |x|,
rmax: rmax(x;y),
rminus: -(x),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
rminus: -(x),
rmax: rmax(x;y),
rabs: |x|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
absval-sqequal-imax,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom
Latex:
\mforall{}[x:Top]. (|x| \msim{} rmax(x;-(x)))
Date html generated:
2016_05_18-AM-07_00_00
Last ObjectModification:
2015_12_28-AM-00_32_49
Theory : reals
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