reserve I for Element of Segm 8,
  S for non empty 1-sorted,
  t for Element of S,
  x for set,
  k for Element of NAT;
 reserve R for Ring, T for InsType of SCM-Instr R;
reserve R for Ring,
  r for Element of R,
  a, b, c, d1, d2 for Data-Location of R,
  i1 for Nat;
reserve s for State of SCM R;

theorem Th10:
  for I being Instruction of SCM R for i being Element of
  SCM-Instr R st i = I for S being SCM-State of R st S = s holds Exec(I,s) =
  SCM-Exec-Res(i,S)
proof
  let I be Instruction of SCM R, i be Element of SCM-Instr R such that
A1: i = I;
  let S be SCM-State of R;
  assume S = s;
  hence Exec(I,s) = ((SCM-Exec R).i qua Element of
   Funcs(product((SCM-VAL R)*SCM-OK),
          product((SCM-VAL R)*SCM-OK))).S by A1,Def1
    .= SCM-Exec-Res(i,S) by SCMRING1:def 15;
end;
