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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.incometax-readings

Lemmas behind operations-research checks src/rainbow/math/lemmas/incometax_readings.clj0 definitions, 2 theorems

General lemmas: incometax 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.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 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math.linear.matrix.affine-general-rate-certificate math.sums.of-nat math.lemmas.one-center

signed/allowance-cases

TheoremFor all inputsNo axiomsSource

signed/allowance-cases :
  (al-g al-A al-t : ℚ)
  (al-hg : 0 ≤ al-g)
  (al-hA : 0 ≤ al-A)
  (al-ht : al-t = data/Bool.rec (fun x₄ => ℚ) (al-g + signed/negate al-A) 0 (signed/decide-at-most al-g al-A))
  → proposition/conjunction (0 ≤ al-t) (conjunction)
  where conjunction := proposition/conjunction (al-g + signed/negate al-A ≤ al-t) (proposition/conjunction (proposition/disjunction (al-t = 0) (al-t = al-g + signed/negate al-A)) (al-t ≤ al-g))

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

signed/tax-cell

TheoremFor all inputsNo axiomsSource

signed/tax-cell :
  (tx-g tx-A tx-B tx-r1 tx-r2 tx-t tx-b tx-h tx-x : ℚ)
  (tx-hg : 0 ≤ tx-g)
  (tx-hA : 0 ≤ tx-A)
  (tx-hB : 0 ≤ tx-B)
  (tx-hr1 : 0 ≤ tx-r1)
  (tx-hr2 : 0 ≤ tx-r2)
  (tx-ht : tx-t = data/Bool.rec (fun x₄ => ℚ) (tx-g + signed/negate tx-A) 0 (signed/decide-at-most tx-g tx-A))
  (tx-hb : tx-b = data/Bool.rec (fun x₈ => ℚ) tx-B tx-t (signed/decide-at-most tx-t tx-B))
  (tx-hh : tx-h = tx-t + signed/negate tx-b)
  (tx-hx : tx-x = tx-r1 · tx-b + tx-r2 · tx-h)
  → proposition/conjunction (conjunction₁) (conjunction)
  where conjunction := proposition/conjunction (proposition/conjunction (proposition/disjunction (tx-b = tx-t) (tx-b = tx-B)) (proposition/conjunction (tx-b ≤ tx-t) (tx-b ≤ tx-B))) (proposition/conjunction (proposition/conjunction (0 ≤ tx-h) (proposition/disjunction (tx-h = 0) (tx-b = tx-B))) (0 ≤ tx-x))
  where conjunction₁ := proposition/conjunction (0 ≤ tx-t) (proposition/conjunction (tx-g + signed/negate tx-A ≤ tx-t) (proposition/conjunction (proposition/disjunction (tx-t = 0) (tx-t = tx-g + signed/negate tx-A)) (tx-t ≤ tx-g)))

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