ProofBytes.byte_put_other.k: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 951-980 of lawful-words@0.1.0.0/proof_bytes.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&start_line=951&end_line=980

import Base
import lawful-words@0.1.0.0/defs.bend as D
import lawful-words@0.1.0.0/proof_nat.bend as N
import lawful-words@0.1.0.0/proof_u32.bend as U

def byte_put_other.k(+w: U32, +i: Nat, +j: Nat, +b: U32, +hb: {U32.is_lt(b, 256) == True{} : Bool}, +hij: {Nat.is_eq(i, j) == False{} : Bool}, +k: Nat) ->
  {D.bit(D.byte(D.put_byte(w, j, b), i), k) == D.bit(D.byte(w, i), k) : Bool}:
  +l = Nat.is_lt(k, 8n)
  +s = Nat.mul(8n, j)
  +p = Nat.add(Nat.mul(8n, i), k)
  +m = U32.shln(255, s)
  +ii = Nat.is_lt(p, 32n)
  +g = Nat.is_le(s, p)
  %Equal.sym(Bool, D.bit(D.byte(D.put_byte(w, j, b), i), k), Bool.and(l, D.bit(D.put_byte(w, j, b), p)), bit_byte(D.put_byte(w, j, b), i, k)) :
    {_ == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.or(U32.and(w, U32.not(m)), U32.shln(b, s)), p), Bool.or(D.bit(U32.and(w, U32.not(m)), p), D.bit(U32.shln(b, s), p)),
      U.bit_or(U32.and(w, U32.not(m)), U32.shln(b, s), p)) :
    {Bool.and(l, _) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.and(w, U32.not(m)), p), Bool.and(D.bit(w, p), D.bit(U32.not(m), p)), U.bit_and(w, U32.not(m), p)) :
    {Bool.and(l, Bool.or(_, D.bit(U32.shln(b, s), p))) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.not(m), p), Bool.and(ii, Bool.not(D.bit(m, p))), U.bit_not(m, p)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), _), D.bit(U32.shln(b, s), p))) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(m, p), Bool.and(g, Bool.and(ii, D.bit(255, Nat.sub(p, s)))), bit_shln(255, s, p)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), Bool.and(ii, Bool.not(_))), D.bit(U32.shln(b, s), p))) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.shln(b, s), p), Bool.and(g, Bool.and(ii, D.bit(b, Nat.sub(p, s)))), bit_shln(b, s, p)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), Bool.and(ii, Bool.not(Bool.and(g, Bool.and(ii, D.bit(255, Nat.sub(p, s))))))), _)) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(255, Nat.sub(p, s)), Nat.is_lt(Nat.sub(p, s), 8n), bit_255(Nat.sub(p, s))) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), Bool.and(ii, Bool.not(Bool.and(g, Bool.and(ii, _))))), Bool.and(g, Bool.and(ii, D.bit(b, Nat.sub(p, s)))))) == D.bit(D.byte(w, i), k) : Bool}
  %Equal.sym(Bool, D.bit(D.byte(w, i), k), Bool.and(l, D.bit(w, p)), bit_byte(w, i, k)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), Bool.and(ii, Bool.not(Bool.and(g, Bool.and(ii, Nat.is_lt(Nat.sub(p, s), 8n)))))), Bool.and(g, Bool.and(ii, D.bit(b, Nat.sub(p, s)))))) == _ : Bool}
  %Equal.sym(Bool, D.bit(w, p), Bool.and(ii, D.bit(w, p)), bit_lt32(w, p)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, p), Bool.and(ii, Bool.not(Bool.and(g, Bool.and(ii, Nat.is_lt(Nat.sub(p, s), 8n)))))), Bool.and(g, Bool.and(ii, D.bit(b, Nat.sub(p, s)))))) == Bool.and(l, _) : Bool}
  other_bits(l, g, ii, D.bit(w, p), Nat.is_lt(Nat.sub(p, s), 8n), D.bit(b, Nat.sub(p, s)),
    hl => hg => N.le_not_lt(8n, Nat.sub(p, s), other_idx(i, j, k, hl, hg, hij)),
    hl => hg => bit_lt_pow(b, 8n, Nat.sub(p, s), %U.is_lt_to_nat(b, 256) : {_ == True{} : Bool}; hb, other_idx(i, j, k, hl, hg, hij)))

Uses (33):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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_eq
  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.mul
  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=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=bit
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=put_byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_255
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_lt32
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_lt_pow
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_shln
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=other_bits
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=other_idx
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_not_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=bit_and
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=bit_not
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=bit_or
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=is_lt_to_nat