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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.capm-normal

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

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

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signed/capm-mean-residual

TheoremFor all inputsNo axiomsSource

signed/capm-mean-residual :
  (mr-n mr-rm mr-al mr-be mr-mm : ℚ)
  (mr-h : mr-al + mr-be · mr-mm = mr-rm)
  → mr-n · mr-rm + signed/negate (mr-al · mr-n + mr-be · (mr-n · mr-mm)) = 0

+ = signed/add0 = signed/zero= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational

signed/capm-residual-term

TheoremFor all inputsNo axiomsSource

signed/capm-residual-term :
  (rt-r rt-rm rt-al rt-be rt-m rt-mm : ℚ)
  (rt-h : rt-al = rt-rm + signed/negate (rt-be · rt-mm))
  → (rt-r + signed/negate (rt-al + rt-be · rt-m)) · (rt-m + signed/negate rt-mm) = (rt-m + signed/negate rt-mm) · (rt-r + signed/negate rt-rm) + signed/negate (rt-be · ((rt-m + signed/negate rt-mm) · (rt-m + signed/negate rt-mm)))

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