PROOFDiv.wm.fn: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_div.bend as PROOFDiv
Lines 73-74 of bend-osdev-word64@0.1.1.0/PROOF_div.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&start_line=73&end_line=74

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 wm.fn(+h: Nat, +n: Nat, +x: Nat, +en: {Nat.add(h, h) == n : Nat}) -> {U.U32Nat.dbl(n, x) == U.U32Nat.dbl(h, U.U32Nat.dbl(h, x)) : Nat}:
  Equal.trans(Nat, U.U32Nat.dbl(n, x), U.U32Nat.dbl(Nat.add(h, h), x), U.U32Nat.dbl(h, U.U32Nat.dbl(h, x)), Equal.cong(Nat, Nat, zz => U.U32Nat.dbl(zz, x), n, Nat.add(h, h), Equal.sym(Nat, Nat.add(h, h), n, en)), Equal.sym(Nat, U.U32Nat.dbl(h, U.U32Nat.dbl(h, x)), U.U32Nat.dbl(Nat.add(h, h), x), UL.dbl_dbl(h, h, x)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl