ProofU32.uq.shr_w: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/proof_u32.bend as ProofU32
Lines 547-556 of bend-osdev-algo@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&start_line=547&end_line=556

import Base

def uq.shr_w(n: Nat, w: Word(n)) -> {Word.to_nat(n, Word.shr(n, w)) == uq.half(Word.to_nat(n, w)) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+ +p:
      match w:
        case WCon{False{}, +t}:
          Equal.trans(Nat, Word.to_nat(1n+p, Word.shr.pad(p, t)), Word.to_nat(p, t), uq.half(Nat.double(Word.to_nat(p, t))), uq.pad(p, t), Equal.sym(Nat, uq.half(Nat.double(Word.to_nat(p, t))), Word.to_nat(p, t), uq.half_dbl(Word.to_nat(p, t))))
        case WCon{True{}, +t}:
          Equal.trans(Nat, Word.to_nat(1n+p, Word.shr.pad(p, t)), Word.to_nat(p, t), uq.half(1n+Nat.double(Word.to_nat(p, t))), uq.pad(p, t), Equal.sym(Nat, uq.half(1n+Nat.double(Word.to_nat(p, t))), Word.to_nat(p, t), uq.half_dbl1(Word.to_nat(p, t))))

Uses (14):
  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=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=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.shr
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shr.pad
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.half
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.half_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.half_dbl1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_u32.bend&name=uq.pad