ProofShift.ns.add_sub_le: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 58-60 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=58&end_line=60

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# k <= n: k + (n - k) = n
def ns.add_sub_le(+k: Nat, +n: Nat, h: {Nat.is_le(k, n) == True{} : Bool}) -> {Nat.add(k, Nat.sub(n, k)) == n : Nat}:
  Equal.trans(Nat, Nat.add(k, Nat.sub(n, k)), Nat.add(Nat.sub(n, k), k), n, UL.nat_add_comm(k, Nat.sub(n, k)), UL.nat_le_witness(k, n, h))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_witness