ProofShift.sv_write: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_shift.bend as ProofShift
Lines 267-276 of lawful-bytes@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&start_line=267&end_line=276

import Base

# Writing that value at j moves the boundary to j + 1.
law sv_write:
  for +xs: List<&2, U32>
  for +jj: Nat
  for +kk: Nat
  for +x: U32
  for +hj: {Nat.is_le(jj, List.length(&2, U32, List.drop(&2, U32, xs, kk))) == True{} : Bool}
  for +hjl: {Nat.is_lt(jj, List.length(&2, U32, xs)) == True{} : Bool}
  for +hx: {List.get(&2, U32, List.drop(&2, U32, xs, kk), jj) == Some{x} : Maybe<&2, U32>}
  {List.set(&2, U32, SV(xs, kk, jj), jj, x) == SV(xs, kk, Nat.add(jj, 1n)) : List<&2, U32>}

Uses (25):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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.is_le
  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=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=set_append_r
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=append_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&name=take_length
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=SV
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=drop_set0
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=sub_self
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=take_snoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_irrefl