Words32.nth0_upd_same: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend as Words32
Lines 68-75 of bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend&start_line=68&end_line=75

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def nth0_upd_same(+xs: List<&2, U32>, +i: Nat, +v: U32, +h: {Nat.is_lt(i, SC.length(U32, xs)) == True{} : Bool}) -> {nth0(SC.update(U32, xs, i, v), i) == v : U32}:
  match xs i:
    case Nil{} _:
      Empty.absurd({nth0(SC.update(U32, Nil{}, i, v), i) == v : U32}, N.lt_zero_absurd(i, h))
    case Con{x, t} 0n:
      {==}
    case Con{x, t} 1n+p:
      nth0_upd_same(t, p, v, h)

Uses (10):
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend&name=nth0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=update