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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.payasbid-readings

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

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

Depends onmath.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 math.rational.nnrat.minmax math.rational.nnrat.farkas-elim-list math.rational.signed.no-zero-divisors math.rational.signed.decide-order math.rational.signed.decide-reflexive math.logic.boolean-and 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math.rational.signed.distributive math.linear.matrix.row-length-shape math.linear.matrix.row-length-decider math.rational.signed.structural-equality math.linear.vector.equivalence math.linear.vector.uniform-clamp math.linear.vector.pointwise-order math.linear.matrix.action-prepend math.linear.matrix.action-associative math.linear.matrix.transpose-multiply math.linear.matrix.transpose-shape math.linear.matrix.transpose-involution math.linear.matrix.transpose-involution-positive math.linear.matrix.transpose-multiply-reverse math.linear.matrix.composable-transpose math.linear.matrix.associativity-counterexample math.linear.matrix.signed-scale math.linear.matrix.signed-scale-right math.linear.matrix.add math.linear.matrix.add-shape math.linear.matrix.prepend-add math.linear.matrix.add-right math.linear.matrix.add-algebra math.linear.matrix.additive-group math.linear.matrix.negate-linear math.linear.matrix.subtract-linear math.linear.matrix.signed-scale-algebra math.linear.matrix.signed-scale-units math.linear.matrix.signed-scale-congruence math.linear.matrix.signed-scale-subtract math.rational.signed.distance-multiply-nonnegative math.rational.signed.vector-sup-distance algorithms.proofs.inner-product math.rational.signed.distance-triangle math.rational.signed.distance-translation math.rational.signed.distance-additive math.linear.vector.dot-distance-bound math.linear.vector.row-sum-lipschitz math.linear.matrix.action-sup-bound math.linear.matrix.signed-scale-order math.linear.matrix.pointwise-order-laws math.linear.matrix.signed-scale-antitone math.linear.matrix.add-order math.linear.matrix.signed-scale-positive math.linear.matrix.signed-scale-sign math.linear.matrix.positive-action math.linear.matrix.transpose-order math.linear.matrix.positive-multiply math.linear.matrix.gram-positive math.linear.matrix.gram-kernel math.linear.matrix.row-gram math.linear.matrix.row-gram-kernel math.linear.vector.norm-pythagorean math.linear.matrix.least-squares-normal math.linear.matrix.least-squares-equality math.linear.matrix.mixed-sign-action math.linear.matrix.mixed-sign-multiply math.linear.matrix.antitone math.linear.matrix.interval-order math.linear.matrix.affine-order math.linear.matrix.linear math.rational.signed.vector-sup-congruence math.finite.vector math.linear.vector.pointwise-order-laws math.linear.vector.add-order math.rational.signed.vector-sup-translation math.linear.matrix.affine-sup-distance math.linear.matrix.row-sum-lipschitz math.linear.matrix.row-sum-fixed-point-uniqueness math.linear.matrix.half-row-sum-fixed-point-uniqueness math.linear.matrix.affine-half-iterate-contraction math.linear.matrix.affine-half-iterate-rate math.rational.signed.geometric-bridge math.linear.matrix.affine-half-iterate-converges math.linear.matrix.affine-strong-row-contraction math.linear.matrix.affine-residual-certificate math.linear.matrix.affine-inverse-gap-certificate math.linear.matrix.affine-general-rate-certificate math.sums.of-nat math.lemmas.one-center

signed/max-reading-from-product

TheoremFor all inputsNo axiomsSource

signed/max-reading-from-product :
  (mx-r mx-a mx-b : ℚ)
  (mx-ha : mx-a ≤ mx-r)
  (mx-hb : mx-b ≤ mx-r)
  (mx-hv : (mx-r + signed/negate mx-a) · (mx-r + signed/negate mx-b) ≤ 0)
  → proposition/disjunction (mx-r = mx-a) (mx-r = mx-b)

+ = signed/add0 = signed/zero= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most

signed/min-reading-from-product

TheoremFor all inputsNo axiomsSource

signed/min-reading-from-product :
  (mn-x mn-a mn-b : ℚ)
  (mn-ha : mn-x ≤ mn-a)
  (mn-hb : mn-x ≤ mn-b)
  (mn-hv : (mn-x + signed/negate mn-a) · (mn-x + signed/negate mn-b) ≤ 0)
  → proposition/disjunction (mn-x = mn-a) (mn-x = mn-b)

+ = signed/add0 = signed/zero= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most

signed/scaled-term-at-most

TheoremFor all inputsNo axiomsSource

signed/scaled-term-at-most :
  (st-x st-c st-d : ℚ)
  (st-hx : 0 ≤ st-x)
  (st-hc : st-c ≤ st-d)
  → st-c · st-x ≤ st-d · st-x

0 = signed/zero· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most