PROOFText.wr.t5: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 160-163 of bend-osdev-word64@0.1.1.0/PROOF_text.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&start_line=160&end_line=163

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 wr.t5(+x0: Nat) -> {U.U32Nat.dbl(x0, 10n) == Nat.mul(U.U32Nat.dbl(x0, 1n), 10n) : Nat}:
  %Equal.sym(Nat, Nat.mul(10n, 1n), Nat.mul(1n, 10n), Equal.sym(Nat, Nat.mul(1n, 10n), Nat.mul(10n, 1n), UL.nat_mul_comm(1n, 10n))) : {U.U32Nat.dbl(x0, _) == Nat.mul(U.U32Nat.dbl(x0, 1n), 10n) : Nat}
  %Equal.sym(Nat, U.U32Nat.dbl(x0, Nat.mul(1n, 10n)), Nat.mul(U.U32Nat.dbl(x0, 1n), 10n), Equal.sym(Nat, Nat.mul(U.U32Nat.dbl(x0, 1n), 10n), U.U32Nat.dbl(x0, Nat.mul(1n, 10n)), UL.dbl_mul_l(x0, 1n, 10n))) : {_ == Nat.mul(U.U32Nat.dbl(x0, 1n), 10n) : Nat}
  {==}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_mul_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_mul_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl