reserve j, k, m for Nat;

theorem Th4:
  for I being Instruction of SCM, k being Element of NAT st
InsCode I = 0 or ... or InsCode I = 5 holds IncAddr (I, k) = I
proof
  let I be Instruction of SCM, k be Element of NAT;
  assume that
A1: InsCode I = 0 or ... or InsCode I = 5;
  per cases by A1;
  suppose InsCode I = 0;
   then I = halt SCM by AMI_5:7;
  hence thesis by COMPOS_0:4;
  end;
  suppose InsCode I = 1;
   then ex da,db being Data-Location st I = da:=db by AMI_5:8;
  hence IncAddr(I,k) = I by COMPOS_0:4;
  end;
  suppose InsCode I = 2;
   then ex da,db being Data-Location st I = AddTo(da,db) by AMI_5:9;
   hence IncAddr(I,k) = I by COMPOS_0:4;
  end;
  suppose InsCode I = 3;
   then ex da,db being Data-Location st I = SubFrom(da,db) by AMI_5:10;
  hence IncAddr(I,k) = I by COMPOS_0:4;
  end;
  suppose InsCode I = 4;
   then ex da,db being Data-Location st I = MultBy(da,db) by AMI_5:11;
   hence IncAddr(I,k) = I by COMPOS_0:4;
  end;
  suppose InsCode I = 5;
   then ex da,db being Data-Location st I = Divide(da,db) by AMI_5:12;
   hence IncAddr(I,k) = I by COMPOS_0:4;
  end;
end;
