Reference · Signed rationals

rainbow.math.rational.signed.distance-additive

Signed rationalssrc/rainbow/math/rational/signed/distance_additive.clj0 definitions, 1 theorems

Paired-addition Lipschitz law for quotient-safe signed distance. The triangle inequality splits through a mixed sum. Right translation cancels the unchanged second addend on the first leg, left translation cancels the unchanged first addend on the second leg, and order congruence transports the resulting upper bound. This is the scalar induction step for dot-product distance estimates. Native, kernel-checked, and axiom-free on D63.

Depends onmath.rational.signed.distance-trianglemath.rational.signed.distance-translation

signed/distance-add :
  (left-first left-second right-first right-second : ℚ)
  → signed/distance (left-first + left-second) (right-first + right-second) ≤ signed/distance left-first right-first + signed/distance left-second right-second