Nuprl Lemma : qabs-positive
∀[r:ℚ]. 0 < |r| supposing ¬(r = 0 ∈ ℚ)
Proof
Definitions occuring in Statement :
qabs: |r|,
qless: r < s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
qpositive-qabs,
qless_witness,
int-subtype-rationals,
qabs_wf,
not_wf,
equal_wf,
rationals_wf,
assert-qpositive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
natural_numberEquality,
applyEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination
Latex:
\mforall{}[r:\mBbbQ{}]. 0 < |r| supposing \mneg{}(r = 0)
Date html generated:
2016_05_15-PM-10_55_12
Last ObjectModification:
2015_12_27-PM-07_52_39
Theory : rationals
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