PROOFChecksum.ckp.cancel: def of bend-osdev-acpi@0.1.2.0
Import: import bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend as PROOFChecksum
Lines 119-123 of bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&start_line=119&end_line=123

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 ckp.cancel(+x: Nat, +a: Nat, +b: Nat, +e: {U.U32Nat.low(8n, Nat.add(x, a)) == U.U32Nat.low(8n, Nat.add(x, b)) : Nat}) -> {U.U32Nat.low(8n, a) == U.U32Nat.low(8n, b) : Nat}:
  %UL.low_add_dbl(8n, a, U.U32Nat.high(8n, Nat.add(x, b))) : {_ == U.U32Nat.low(8n, b) : Nat}
  %UL.low_add_dbl(8n, b, U.U32Nat.high(8n, Nat.add(x, a))) : {U.U32Nat.low(8n, Nat.add(a, U.U32Nat.dbl(8n, U.U32Nat.high(8n, Nat.add(x, b))))) == _ : Nat}
  %UL.nat_add_cancel(x, Nat.add(a, U.U32Nat.dbl(8n, U.U32Nat.high(8n, Nat.add(x, b)))), Nat.add(b, U.U32Nat.dbl(8n, U.U32Nat.high(8n, Nat.add(x, a)))), ckp.cr(x, a, b, e)) : {U.U32Nat.low(8n, Nat.add(a, U.U32Nat.dbl(8n, U.U32Nat.high(8n, Nat.add(x, b))))) == U.U32Nat.low(8n, _) : Nat}
  {==}

Uses (8):
  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-acpi@0.1.2.0/PROOF_checksum.bend&name=ckp.cr
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=low_add_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_cancel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.high
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.low