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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.edf-readings

Lemmas behind operations-research checks src/rainbow/math/lemmas/edf_readings.clj0 definitions, 1 theorems

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

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signed/edf-demand-bound

TheoremFor all inputsNo axiomsSource

signed/edf-demand-bound :
  (ed-c ed-t ed-u ed-k : ℕ → ℚ) (ed-n : ℕ) (ed-uu ed-l : ℚ)
  (ed-hu : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx ed-n), 0 ≤ ed-u idx)
  (ed-hc : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx ed-n), ed-u idx · ed-t idx = ed-c idx)
  (ed-hsum : ed-uu = signed/expr-sum-value ed-u ed-n)
  (ed-h1 : ed-uu ≤ 1)
  (ed-hk : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx ed-n), ed-k idx · ed-t idx ≤ ed-l)
  (ed-hl : 0 ≤ ed-l)
  → signed/expr-sum-value (fun kc-i => ed-k kc-i · ed-c kc-i) ed-n ≤ ed-l

0 = signed/zero1 = signed/one= = signed/equivalent: equality of rational values· = signed/multiplyℕ = data/Natℚ = signed/SignedRational≤ = signed/at-most