Arith.le_add_cancel: 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 62-68 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=62&end_line=68

import Base

# d + x <= d + y is x <= y
def le_add_cancel(+d: Nat, +x: Nat, +y: Nat) -> {Nat.is_le(Nat.add(d, x), Nat.add(d, y)) == Nat.is_le(x, y) : Bool}:
  match d:
    case 0n:
      {==}
    case 1n+ +dp:
      le_add_cancel(dp, x, y)

Uses (4):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le