ProofBytes.byte_put_same.k: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 839-870 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=839&end_line=870

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

# The bits of put_byte(w, j, b) at byte j, bit k.
def byte_put_same.k(+w: U32, +j: Nat, +b: U32, +hj: {Nat.is_lt(j, 4n) == True{} : Bool}, +hb: {U32.is_lt(b, 256) == True{} : Bool}, +k: Nat) ->
  {D.bit(D.byte(D.put_byte(w, j, b), j), k) == D.bit(b, k) : Bool}:
  +l = Nat.is_lt(k, 8n)
  +s = Nat.mul(8n, j)
  +i = Nat.add(s, k)
  +m = U32.shln(255, s)
  +ii = Nat.is_lt(i, 32n)
  %Equal.sym(Bool, D.bit(D.byte(D.put_byte(w, j, b), j), k), Bool.and(l, D.bit(D.put_byte(w, j, b), i)), bit_byte(D.put_byte(w, j, b), j, k)) :
    {_ == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(U32.or(U32.and(w, U32.not(m)), U32.shln(b, s)), i), Bool.or(D.bit(U32.and(w, U32.not(m)), i), D.bit(U32.shln(b, s), i)),
      U.bit_or(U32.and(w, U32.not(m)), U32.shln(b, s), i)) :
    {Bool.and(l, _) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(U32.and(w, U32.not(m)), i), Bool.and(D.bit(w, i), D.bit(U32.not(m), i)), U.bit_and(w, U32.not(m), i)) :
    {Bool.and(l, Bool.or(_, D.bit(U32.shln(b, s), i))) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(U32.not(m), i), Bool.and(ii, Bool.not(D.bit(m, i))), U.bit_not(m, i)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), _), D.bit(U32.shln(b, s), i))) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(m, i), Bool.and(Nat.is_le(s, i), Bool.and(ii, D.bit(255, Nat.sub(i, s)))), bit_shln(255, s, i)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(_))), D.bit(U32.shln(b, s), i))) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(U32.shln(b, s), i), Bool.and(Nat.is_le(s, i), Bool.and(ii, D.bit(b, Nat.sub(i, s)))), bit_shln(b, s, i)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(Bool.and(Nat.is_le(s, i), Bool.and(ii, D.bit(255, Nat.sub(i, s))))))), _)) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, Nat.is_le(s, i), True{}, N.le_add_r(s, k)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(Bool.and(_, Bool.and(ii, D.bit(255, Nat.sub(i, s))))))),
      Bool.and(_, Bool.and(ii, D.bit(b, Nat.sub(i, s)))))) == D.bit(b, k) : Bool}
  %Equal.sym(Nat, Nat.sub(i, s), k, N.sub_add_l(s, k)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(Bool.and(True{}, Bool.and(ii, D.bit(255, _)))))),
      Bool.and(True{}, Bool.and(ii, D.bit(b, _))))) == D.bit(b, k) : Bool}
  %Equal.sym(Bool, D.bit(255, k), l, bit_255(k)) :
    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(Bool.and(True{}, Bool.and(ii, _))))),
      Bool.and(True{}, Bool.and(ii, D.bit(b, k))))) == D.bit(b, k) : Bool}
  put_bits(l, ii, D.bit(w, i), D.bit(b, k), hk => idx32(j, k, hj, hk),
    e => bit_lt_pow(b, 8n, k, %U.is_lt_to_nat(b, 256) : {_ == True{} : Bool}; hb, N.not_lt_le(k, 8n, e)))

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_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_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=idx32
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=put_bits
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=not_lt_le
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=sub_add_l
  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