Words32.nth0_upd_other: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/words32.bend as Words32
Lines 77-88 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/words32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/words32.bend&start_line=77&end_line=88

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def nth0_upd_other(+xs: List<&2, U32>, +i: Nat, +j: Nat, +v: U32, +h: {Nat.is_eq(i, j) == False{} : Bool}) -> {nth0(SC.update(U32, xs, i, v), j) == nth0(xs, j) : U32}:
  match xs i j:
    case Nil{} _ _:
      {==}
    case Con{x, r} 0n 0n:
      Empty.absurd({nth0(SC.update(U32, Con{x, r}, 0n, v), 0n) == nth0(Con{x, r}, 0n) : U32}, L.true_false(h))
    case Con{x, r} 0n 1n+q:
      {==}
    case Con{x, r} 1n+p 0n:
      {==}
    case Con{x, r} 1n+p 1n+q:
      nth0_upd_other(r, p, q, v, h)

Uses (9):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=true_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/words32.bend&name=nth0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=update