def byte_put_other.k

lawful-words@0.1.0.0 · proof_bytes.bend:951

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

951def 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) ->
952  {D.bit(D.byte(D.put_byte(w, j, b), i), k) == D.bit(D.byte(w, i), k) : Bool}:
953  +l = Nat.is_lt(k, 8n)
954  +s = Nat.mul(8n, j)
955  +p = Nat.add(Nat.mul(8n, i), k)
956  +m = U32.shln(255, s)
957  +ii = Nat.is_lt(p, 32n)
958  +g = Nat.is_le(s, p)
959  %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)) :
960    {_ == D.bit(D.byte(w, i), k) : Bool}
961  %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)),
962      U.bit_or(U32.and(w, U32.not(m)), U32.shln(b, s), p)) :
963    {Bool.and(l, _) == D.bit(D.byte(w, i), k) : Bool}
964  %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)) :
965    {Bool.and(l, Bool.or(_, D.bit(U32.shln(b, s), p))) == D.bit(D.byte(w, i), k) : Bool}
966  %Equal.sym(Bool, D.bit(U32.not(m), p), Bool.and(ii, Bool.not(D.bit(m, p))), U.bit_not(m, p)) :
967    {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}
968  %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)) :
969    {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}
970  %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)) :
971    {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}
972  %Equal.sym(Bool, D.bit(255, Nat.sub(p, s)), Nat.is_lt(Nat.sub(p, s), 8n), bit_255(Nat.sub(p, s))) :
973    {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}
974  %Equal.sym(Bool, D.bit(D.byte(w, i), k), Bool.and(l, D.bit(w, p)), bit_byte(w, i, k)) :
975    {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}
976  %Equal.sym(Bool, D.bit(w, p), Bool.and(ii, D.bit(w, p)), bit_lt32(w, p)) :
977    {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}
978  other_bits(l, g, ii, D.bit(w, p), Nat.is_lt(Nat.sub(p, s), 8n), D.bit(b, Nat.sub(p, s)),
979    hl => hg => N.le_not_lt(8n, Nat.sub(p, s), other_idx(i, j, k, hl, hg, hij)),
980    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)))