reserve n for Nat,
        p,p1,p2 for Point of TOP-REAL n,
        x for Real;
reserve n,m for non zero Nat;
reserve i,j for Nat;
reserve f for PartFunc of REAL-NS m,REAL-NS n;
reserve g for PartFunc of REAL m,REAL n;
reserve h for PartFunc of REAL m,REAL;
reserve x for Point of REAL-NS m;
reserve y for Element of REAL m;
reserve X for set;

theorem Th3:
((0*j) /^ i) = 0*((j-'i))
proof
  per cases;
  suppose i <= j;
    hence thesis by Lm3;
  end;
  suppose i > j;
    hence thesis by Lm4;
  end;
end;
