Nuprl Lemma : qabs-nonneg
∀[r:ℚ]. (0 ≤ |r|)
Proof
Definitions occuring in Statement :
qabs: |r|,
qle: r ≤ s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q
Lemmas referenced :
zero-qle-qabs,
qle_witness,
int-subtype-rationals,
qabs_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
applyEquality,
sqequalRule,
independent_functionElimination
Latex:
\mforall{}[r:\mBbbQ{}]. (0 \mleq{} |r|)
Date html generated:
2016_05_15-PM-11_01_25
Last ObjectModification:
2015_12_27-PM-07_48_07
Theory : rationals
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