PROOF.un.so: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1487-1496 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=1487&end_line=1496

import Base

# Word.shl.out is the bit going out and the shifted word
def un.so(n: Nat, +c: Bool, +w: Word(n)) -> {Word.shl.out(n, c, w) == (un.topc(n, c, w), Word.shl.put(n, c, w)) : Bool & Word(n)}:
  match n:
    case 0n:
      {==}
    case 1n+ +p:
      match w:
        case WCon{+x, +t}:
          %Equal.sym(Bool & Word(p), Word.shl.out(p, x, t), (un.topc(p, x, t), Word.shl.put(p, x, t)), un.so(p, x, t)) : {Word.shl.out.con(p, c, _) == (un.topc(p, x, t), WCon{c, Word.shl.put(p, x, t)}) : Bool & Word(1n+p)}
          {==}

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.out
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.out.con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.put
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.topc