PROOF.h.isz_put: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1976-1986 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=1976&end_line=1986

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool

def h.isz_put(n: Nat, t: Word(n), e: {h.isz(n, t) == True{} : Bool})
  -> {h.isz(n, Word.shl.put(n, False{}, t)) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+p:
      match t:
        case WCon{True{}, t2}:
          Empty.absurd({h.isz(1n+p, Word.shl.put(1n+p, False{}, WCon{True{}, t2})) == True{} : Bool}, MBool.false_ne_true()(e))
        case WCon{False{}, t2}:
          h.isz_put(p, t2, e)

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.put
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.isz
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=false_ne_true