Nuprl Lemma : qabs-qmul-case2
∀[r,s,a:ℚ]. (|(a * r) - a * s| = (|r - s| * |a|) ∈ ℚ)
Proof
Definitions occuring in Statement :
qabs: |r|,
qsub: r - s,
qmul: r * s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
qabs_wf,
rationals_wf,
qsub_wf,
qmul_wf,
qmul_com,
iff_weakening_equal,
qabs-qmul-case1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[r,s,a:\mBbbQ{}]. (|(a * r) - a * s| = (|r - s| * |a|))
Date html generated:
2018_05_21-PM-11_53_21
Last ObjectModification:
2017_07_26-PM-06_45_36
Theory : rationals
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