Arith.div_le: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as Arith
Lines 121-127 of bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&start_line=121&end_line=127

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

# a quotient never exceeds its dividend
def div_le(+a: Nat, +d: Nat) -> {Nat.is_le(Nat.div(a, d), a) == True{} : Bool}:
  match d:
    case 0n:
      N.zero_le(a)
    case 1n+bp:
      go_le(a, bp, 0n, 0n)

Uses (6):
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&name=go_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=zero_le