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;
