def byte_put_same.k

lawful-words@0.1.0.0 · proof_bytes.bend:839

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

839# The bits of put_byte(w, j, b) at byte j, bit k.
840def 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) ->
841  {D.bit(D.byte(D.put_byte(w, j, b), j), k) == D.bit(b, k) : Bool}:
842  +l = Nat.is_lt(k, 8n)
843  +s = Nat.mul(8n, j)
844  +i = Nat.add(s, k)
845  +m = U32.shln(255, s)
846  +ii = Nat.is_lt(i, 32n)
847  %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)) :
848    {_ == D.bit(b, k) : Bool}
849  %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)),
850      U.bit_or(U32.and(w, U32.not(m)), U32.shln(b, s), i)) :
851    {Bool.and(l, _) == D.bit(b, k) : Bool}
852  %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)) :
853    {Bool.and(l, Bool.or(_, D.bit(U32.shln(b, s), i))) == D.bit(b, k) : Bool}
854  %Equal.sym(Bool, D.bit(U32.not(m), i), Bool.and(ii, Bool.not(D.bit(m, i))), U.bit_not(m, i)) :
855    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), _), D.bit(U32.shln(b, s), i))) == D.bit(b, k) : Bool}
856  %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)) :
857    {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}
858  %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)) :
859    {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}
860  %Equal.sym(Bool, Nat.is_le(s, i), True{}, N.le_add_r(s, k)) :
861    {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))))))),
862      Bool.and(_, Bool.and(ii, D.bit(b, Nat.sub(i, s)))))) == D.bit(b, k) : Bool}
863  %Equal.sym(Nat, Nat.sub(i, s), k, N.sub_add_l(s, k)) :
864    {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, _)))))),
865      Bool.and(True{}, Bool.and(ii, D.bit(b, _))))) == D.bit(b, k) : Bool}
866  %Equal.sym(Bool, D.bit(255, k), l, bit_255(k)) :
867    {Bool.and(l, Bool.or(Bool.and(D.bit(w, i), Bool.and(ii, Bool.not(Bool.and(True{}, Bool.and(ii, _))))),
868      Bool.and(True{}, Bool.and(ii, D.bit(b, k))))) == D.bit(b, k) : Bool}
869  put_bits(l, ii, D.bit(w, i), D.bit(b, k), hk => idx32(j, k, hj, hk),
870    e => bit_lt_pow(b, 8n, k, %U.is_lt_to_nat(b, 256) : {_ == True{} : Bool}; hb, N.not_lt_le(k, 8n, e)))