PROOF.ur.r31: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1678-1680 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=1678&end_line=1680

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

def ur.r31(+x0: Nat) -> {Nat.double(x0) == Nat.add(x0, x0) : Nat}:
  %Equal.sym(Nat, Nat.double(x0), Nat.add(x0, x0), Laws.nat_double(x0)) : {_ == Nat.add(x0, x0) : Nat}
  {==}

Uses (5):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_double