def byte_shln_high.k

lawful-words@0.1.0.0 · proof_bytes.bend:716

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

716def byte_shln_high.k(+w: U32, +s: Nat, +j: Nat, +hs: {Nat.is_le(s, j) == True{} : Bool}, +hj: {Nat.is_lt(j, 4n) == True{} : Bool}, +k: Nat) ->
717  {D.bit(D.byte(U32.shln(w, Nat.mul(8n, s)), j), k) == D.bit(D.byte(w, Nat.sub(j, s)), k) : Bool}:
718  +l = Nat.is_lt(k, 8n)
719  +i = Nat.add(Nat.mul(8n, j), k)
720  +s8 = Nat.mul(8n, s)
721  +x = D.bit(w, Nat.add(Nat.mul(8n, Nat.sub(j, s)), k))
722  %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)) :
723    {_ == D.bit(D.byte(w, Nat.sub(j, s)), k) : Bool}
724  %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)) :
725    {Bool.and(l, _) == D.bit(D.byte(w, Nat.sub(j, s)), k) : Bool}
726  %Equal.sym(Bool, D.bit(D.byte(w, Nat.sub(j, s)), k), Bool.and(l, x), bit_byte(w, Nat.sub(j, s), k)) :
727    {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}
728  %Equal.sym(Bool, Nat.is_le(s8, i), True{}, N.le_trans(s8, Nat.mul(8n, j), i, N.le_mul_l(8n, s, j, hs), N.le_add_r(Nat.mul(8n, j), k))) :
729    {Bool.and(l, Bool.and(_, Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8))))) == Bool.and(l, x) : Bool}
730  %Equal.sym(Nat, Nat.sub(i, s8), Nat.add(Nat.mul(8n, Nat.sub(j, s)), k), idx_sub(s, j, k, hs)) :
731    {Bool.and(l, Bool.and(True{}, Bool.and(Nat.is_lt(i, 32n), D.bit(w, _)))) == Bool.and(l, x) : Bool}
732  bimp(l, Nat.is_lt(i, 32n), x, hk => idx32(j, k, hj, hk))