def byte_shln_low.k

lawful-words@0.1.0.0 · proof_bytes.bend:691

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

691def byte_shln_low.k(+w: U32, +s: Nat, +j: Nat, +hj: {Nat.is_lt(j, s) == True{} : Bool}, +k: Nat) ->
692  {D.bit(D.byte(U32.shln(w, Nat.mul(8n, s)), j), k) == D.bit(0, k) : Bool}:
693  +l = Nat.is_lt(k, 8n)
694  +i = Nat.add(Nat.mul(8n, j), k)
695  +s8 = Nat.mul(8n, s)
696  %Equal.sym(Bool, D.bit(D.byte(U32.shln(w, s8), j), k), Bool.and(l, D.bit(U32.shln(w, s8), i)), bit_byte(U32.shln(w, s8), j, k)) :
697    {_ == D.bit(0, k) : Bool}
698  %Equal.sym(Bool, D.bit(U32.shln(w, s8), i), Bool.and(Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8)))), bit_shln(w, s8, i)) :
699    {Bool.and(l, _) == D.bit(0, k) : Bool}
700  %Equal.sym(Bool, D.bit(0, k), False{}, bit_zero(k)) :
701    {Bool.and(l, Bool.and(Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8))))) == _ : Bool}
702  blow(l, Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8))),
703    hk => lt_not_le(i, s8, N.lt_le_trans(i, Nat.mul(8n, 1n+j), s8, lt_mul8(j, k, hk),
704      N.le_mul_l(8n, 1n+j, s, %Equal.sym(Bool, Nat.is_le(1n+j, s), Nat.is_lt(j, s), N.le_succ_lt(j, s)) : {_ == True{} : Bool}; hj))))