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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.prf-readings

Lemmas behind operations-research checks src/rainbow/math/lemmas/prf_readings.clj0 definitions, 3 theorems

General lemmas: prf readings. The mathematical facts the corresponding checks rest on, each checked by the kernel.

Depends onmath.lemmas.pcmax-lower-bound math.lemmas.kmeans-nearest math.rational.signed.lp-duality-on math.lemmas.indep-set-dual math.lemmas.mmck-unique math.lemmas.cpm-makespan math.lemmas.ncyc-infeasible math.sums.value-append math.nat.infinite math.rational.nnrat.identities math.nat.at-most-cancellation math.rational.nnrat.order-equivalence math.rational.nnrat.archimedean math.rational.nnrat.add-monotone math.rational.nnrat.add-cancellation math.rational.nnrat.additive-reassociation math.rational.signed.order-transitivity math.rational.signed.convergence math.rational.signed.order-respects math.rational.signed.limit-uniqueness math.rational.signed.strict-order math.rational.signed.multiply math.rational.nnrat.multiply-commute math.rational.nnrat.product-reassociation math.rational.nnrat.distribute-right math.rational.nnrat.ring math.rational.nnrat.multiply-monotone math.rational.nnrat.order-difference math.rational.signed.multiply-order math.rational.signed.equivalence-laws 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signed/positive-of-at-least-one

TheoremFor all inputsNo axiomsSource

signed/positive-of-at-least-one :
  (po-x : ℚ)
  (po-h : 1 ≤ po-x)
  → 0 < po-x

0 = signed/zero1 = signed/one< = signed/less-thanℚ = signed/SignedRational≤ = signed/at-most

signed/f1-harmonic

TheoremFor all inputsNo axiomsSource

signed/f1-harmonic :
  (fh-t fh-fp fh-fn fh-p fh-r fh-f : ℚ)
  (fh-hp : fh-p · (fh-t + fh-fp) = fh-t)
  (fh-hr : fh-r · (fh-t + fh-fn) = fh-t)
  (fh-hf : fh-f · (signed/from-nnrat 2 · fh-t + (fh-fp + fh-fn)) = signed/from-nnrat 2 · fh-t)
  (fh-ha : 1 ≤ fh-t + fh-fp)
  (fh-hb : 1 ≤ fh-t + fh-fn)
  → fh-f · (fh-p + fh-r) = fh-p · fh-r + fh-p · fh-r

+ = signed/add1 = signed/one= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most

signed/indicator-cell-split

TheoremFor all inputsNo axiomsSource

signed/indicator-cell-split :
  (sp-y sp-h : ℚ)
  → proposition/conjunction (sp-y · sp-h + (1 + signed/negate sp-y) · sp-h = sp-h) (sp-y · sp-h + sp-y · (1 + signed/negate sp-h) = sp-y)

+ = signed/add1 = signed/one= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational