
theorem Th3:
  for I1, I2 being Instruction of SCM
  for F being total
   NAT-defined (the InstructionsF of SCM)-valued Function
   st <%I1%>^<%I2%> c= F
   holds F.0 = I1 & F.1 = I2
proof
  let I1, I2 be Instruction of SCM;
  let F be total
   NAT-defined the InstructionsF of SCM-valued Function such that
A1: <%I1%>^<%I2%> c= F;
  set ins = <%I1%>^<%I2%>;
A2: ins = <%I1, I2%>;
  then
A3: ins.1 = I2;
A4:  ins.0 = I1 by A2;
    len ins = 2 by A2,AFINSQ_1:38;
   then 0 in dom ins & 1 in dom ins by CARD_1:50,TARSKI:def 2;
  hence thesis by A1,A3,A4,GRFUNC_1:2;
end;
