U32.internal_shl_out: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 791-807 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=791&end_line=807

import Base

def internal_shl_out(n: Nat, c: Bool, w: Word(n)) -> {internal_shl_val(n, Nat.pow(2n, n), Word.shl.out(n, c, w)) == Nat.add(internal_bv(c), Nat.double(Word.to_nat(n, w))) : Nat}:
  match n:
    case 0n:
      match c:
        case False{}:
          match w:
            case WNil{}:
              {==}
        case True{}:
          match w:
            case WNil{}:
              {==}
    case 1n++p:
      match w:
        case WCon{+b, +t}:
          %internal_to_nat_con(p, b, t) : {internal_shl_val(1n+p, Nat.pow(2n, 1n+p), Word.shl.out(1n+p, c, WCon{b, t})) == Nat.add(internal_bv(c), Nat.double(_)) : Nat}
          internal_shl_con(p, c, Word.shl.out(p, b, t), Nat.add(internal_bv(b), Nat.double(Word.to_nat(p, t))), internal_shl_out(p, b, 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=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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  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.Nil
  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.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_bv
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_shl_con
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_shl_val
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_to_nat_con