LAWS.u32_shln_value: law of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/LAWS.bend as LAWS
Lines 204-209 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=204&end_line=209

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

law u32_shln_value:
  for +a: U32
  for +k: Nat
  for +c: U32
  for +h: {Nat.is_le(U.U32Nat.dbl(k, U32.to_nat(a)), U32.to_nat(c)) == True{} : Bool}
  {U32.to_nat(U32.shln(a, k)) == U.U32Nat.dbl(k, U32.to_nat(a)) : Nat}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.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.double
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_shl_value
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.double_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.le_double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl