Nat.le_div_iff_mul_le: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 941-946 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=941&end_line=946

import Base

# A quotient is compared by multiplying back: n <= a / (1 + b) tests as n * (1 + b) <= a.
law le_div_iff_mul_le:
  for n: Nat
  for +a: Nat
  for +b: Nat
  {Nat.is_le(n, Nat.div(a, 1n+b)) == Nat.is_le(Nat.mul(n, 1n+b), a) : Bool}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_div_le_step
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_div_zero_le