Arith.le_div: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as Arith
Lines 82-86 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&start_line=82&end_line=86

import Base

# x <= n / d is x d <= n   (Mathlib Nat.le_div_iff_mul_le)
def le_div(+bp: Nat, +x: Nat, +n: Nat) -> {Nat.is_le(x, Nat.div(n, 1n+bp)) == Nat.is_le(Nat.mul(x, 1n+bp), n) : Bool}:
  +e = dm_eq(bp, n)
  %Equal.sym(Nat, n, Nat.add(Nat.mul(Nat.div(n, 1n+bp), 1n+bp), Nat.mod(n, 1n+bp)), e) : {Nat.is_le(x, Nat.div(n, 1n+bp)) == Nat.is_le(Nat.mul(x, 1n+bp), _) : Bool}
  le_div_g(x, Nat.div(n, 1n+bp), bp, Nat.mod(n, 1n+bp), dm_lt(bp, n))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=dm_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=dm_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=le_div_g