ProofShift.ns.dmk: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 202-203 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=202&end_line=203

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

def ns.dmk(+n: Nat, +k: Nat, +x: Nat, h: {Nat.is_le(k, n) == True{} : Bool}) -> {U.U32Nat.dbl(Nat.sub(n, k), U.U32Nat.dbl(k, x)) == U.U32Nat.dbl(n, x) : Nat}:
  Equal.trans(Nat, U.U32Nat.dbl(Nat.sub(n, k), U.U32Nat.dbl(k, x)), U.U32Nat.dbl(k, U.U32Nat.dbl(Nat.sub(n, k), x)), U.U32Nat.dbl(n, x), UL.dbl_comm(Nat.sub(n, k), k, x), ns.dkm(n, k, x, 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.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=dbl_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ns.dkm