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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.unifpx-readings

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

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

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math.linear.matrix.affine-general-rate-certificate math.sums.of-nat math.lemmas.one-center

signed/prefix-units-bound

TheoremFor all inputsNo axiomsSource

signed/prefix-units-bound :
  (pu-x pu-q pu-Q pu-r : ℕ → ℚ) (pu-S : ℚ) (pu-M : ℕ)
  (pu-hxq : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx pu-M), pu-x idx ≤ pu-q idx)
  (pu-hxr : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx pu-M), pu-x idx ≤ pu-r idx)
  (pu-hr : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx pu-M), proposition/disjunction (pu-r idx = 0) (pu-r idx = pu-S + signed/negate (pu-Q idx)))
  (pu-hQ : ∀ (idx : ℕ), ∀ (bound : nat/strict-below idx pu-M), pu-Q idx = signed/expr-sum-value pu-q idx)
  (pu-hS : 0 ≤ pu-S)
  → proposition/conjunction (signed/expr-sum-value pu-x pu-M ≤ signed/expr-sum-value pu-q pu-M) (signed/expr-sum-value pu-x pu-M ≤ pu-S)

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