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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.cournot-readings

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

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

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signed/cournot-best-response

TheoremFor all inputsNo axiomsSource

signed/cournot-best-response :
  (cb-a cb-b cb-q cb-qi cb-c cb-p cb-x : ℚ)
  (cb-hp : cb-p = cb-a + signed/negate (cb-b · cb-q))
  (cb-hf : cb-p + (signed/negate (cb-b · cb-qi) + signed/negate cb-c) = 0)
  (cb-hb : 0 ≤ cb-b)
  → cb-x · (cb-a + signed/negate (cb-b · (cb-q + signed/negate cb-qi + cb-x)) + signed/negate cb-c) ≤ cb-qi · (cb-a + signed/negate (cb-b · (cb-q + signed/negate cb-qi + cb-qi)) + signed/negate cb-c)

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