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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.sir-readings

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

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

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math.linear.matrix.affine-general-rate-certificate math.sums.of-nat math.lemmas.one-center math.rational.signed.multiply-associative

signed/sir-step-identities

TheoremFor all inputsNo axiomsSource

signed/sir-step-identities :
  (si-s si-i si-r si-s1 si-i1 si-r1 si-b si-g : ℚ)
  (sh-s : si-s1 = si-s + signed/negate (si-b · (si-s · si-i)))
  (sh-i : si-i1 = si-i + (si-b · (si-s · si-i) + signed/negate (si-g · si-i)))
  (sh-r : si-r1 = si-r + si-g · si-i)
  → proposition/conjunction (si-s1 + (si-i1 + si-r1) = si-s + (si-i + si-r)) (si-i1 + signed/negate si-i = si-i · (si-b · si-s + signed/negate si-g))

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

signed/sir-step-nonnegative

TheoremFor all inputsNo axiomsSource

signed/sir-step-nonnegative :
  (sn-s sn-i sn-r sn-s1 sn-i1 sn-r1 sn-b sn-g : ℚ)
  (sh-s : sn-s1 = sn-s + signed/negate (sn-b · (sn-s · sn-i)))
  (sh-i : sn-i1 = sn-i + (sn-b · (sn-s · sn-i) + signed/negate (sn-g · sn-i)))
  (sh-r : sn-r1 = sn-r + sn-g · sn-i)
  (sn-hb : 0 ≤ sn-b)
  (sn-hg : 0 ≤ sn-g)
  (sn-hg1 : sn-g ≤ 1)
  (sn-hbi : sn-b · sn-i ≤ 1)
  (sn-hn : proposition/conjunction (0 ≤ sn-s) (conjunction₁))
  → proposition/conjunction (0 ≤ sn-s1) (conjunction)
  where conjunction := proposition/conjunction (0 ≤ sn-i1) (0 ≤ sn-r1)
  where conjunction₁ := proposition/conjunction (0 ≤ sn-i) (0 ≤ sn-r)

+ = signed/add0 = signed/zero1 = signed/one= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most