Reference · Signed rationals

rainbow.math.rational.signed.half-scale-subtract-self

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

B6e of the limit-reciprocal arc: subtracting half of a value from itself leaves half. signed/half-scale-subtract-self : value - (1/2 * value) ~ 1/2 * value where 1/2 * value = smul (from-nnrat nnrat/half) value. Reuses the existing signed/half-scale-add-self (1/2 v + 1/2 v ~ v): rewrite value as (h + h), then (h + h) - h ~ h by associativity + subtract-self + add-zero-right. The assembly instantiates value = |L|, so convergent-bounded-below at radius (1/2)|L| yields (1/2)|L| <= |s n| (a fixed positive lower bound). Axiom-free; additive; does not touch the LP checker.

Depends onmath.linear.matrix.half-row-sum-fixed-point-uniquenessmath.rational.signed.add-associativemath.linear.vector.dot-subtractmath.rational.signed.unit-lawsmath.rational.signed.kkt-sufficiency

signed/half-scale-subtract-self :
  (value : ℚ)
  → value - signed/from-nnrat nnrat/half · value = signed/from-nnrat nnrat/half · value