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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.salesq-readings

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

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

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signed/shortfall-cases

TheoremFor all inputsNo axiomsSource

signed/shortfall-cases :
  (sc-t sc-a sc-s : ℚ)
  (sc-h : sc-s = data/Bool.rec (fun x₄ => ℚ) 0 (sc-t + signed/negate sc-a) (signed/decide-at-most sc-a sc-t))
  → proposition/conjunction (0 ≤ sc-s) (conjunction)
  where conjunction := proposition/conjunction (sc-t + signed/negate sc-a ≤ sc-s) (proposition/conjunction (proposition/disjunction (sc-s = 0) (sc-s = sc-t + signed/negate sc-a)) (∀ (sf-met : sc-t ≤ sc-a), sc-s = 0))

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

signed/on-target-cases

TheoremFor all inputsNo axiomsSource

signed/on-target-cases :
  (fc-t fc-a fc-f : ℚ)
  (fc-h : fc-f = data/Bool.rec (fun x₄ => ℚ) 0 1 (signed/decide-at-most fc-t fc-a))
  → proposition/disjunction (conjunction) (conjunction₁)
  where conjunction := proposition/conjunction (fc-f = 1) (fc-t ≤ fc-a)
  where conjunction₁ := proposition/conjunction (fc-f = 0) (fc-a ≤ fc-t)

0 = signed/zero1 = signed/one= = signed/equivalent: equality of rational valuesℚ = signed/SignedRational≤ = signed/at-most