LAWS.dbl_nowrap: law of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/LAWS.bend as LAWS
Lines 394-403 of bend-osdev-u32@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&start_line=394&end_line=403

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

law dbl_nowrap:
  for +n: Nat
  for +k: Nat
  for +r: Nat
  for +p: Nat
  for +z: Nat
  for e: {Nat.add(r, U.U32Nat.dbl(n, k)) == p : Nat}
  for h: {Nat.is_le(p, z) == True{} : Bool}
  for hz: {Nat.is_lt(z, U.U32Nat.dbl(n, 1n)) == True{} : Bool}
  {r == p : Nat}

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_witness
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_lt_witness
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_succ_add_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ur.r3
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl