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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.wab-mean

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

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

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signed/weighted-mean-upper

TheoremFor all inputsNo axiomsSource

signed/weighted-mean-upper :
  (wu-w wu-a : ℕ → ℚ) (wu-n : ℕ) (wu-u wu-c wu-bigw : ℚ)
  (wu-hw : wu-bigw = signed/expr-sum-value wu-w wu-n)
  (wu-hc : wu-c · wu-bigw = signed/expr-sum-value (fun mo-i => wu-w mo-i · wu-a mo-i) wu-n)
  (wu-pos : 0 < wu-bigw)
  (wu-b : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx wu-n), wu-w idx · (wu-a idx + signed/negate wu-u) ≤ 0)
  → wu-c ≤ wu-u

+ = signed/add0 = signed/zero< = signed/less-than= = signed/equivalent: equality of rational values· = signed/multiplyℕ = data/Natℚ = signed/SignedRational≤ = signed/at-most

signed/weighted-mean-lower

TheoremFor all inputsNo axiomsSource

signed/weighted-mean-lower :
  (wl-w wl-a : ℕ → ℚ) (wl-n : ℕ) (wl-l wl-c wl-bigw : ℚ)
  (wl-hw : wl-bigw = signed/expr-sum-value wl-w wl-n)
  (wl-hc : wl-c · wl-bigw = signed/expr-sum-value (fun mo-i => wl-w mo-i · wl-a mo-i) wl-n)
  (wl-pos : 0 < wl-bigw)
  (wl-b : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx wl-n), wl-w idx · (wl-l + signed/negate (wl-a idx)) ≤ 0)
  → wl-l ≤ wl-c

+ = signed/add0 = signed/zero< = signed/less-than= = signed/equivalent: equality of rational values· = signed/multiplyℕ = data/Natℚ = signed/SignedRational≤ = signed/at-most