reserve i,i1,i2,i3,i4,i5,j,r,a,b,x,y for Integer,
  d,e,k,n for Nat,
  fp,fk for FinSequence of INT,
  f,f1,f2 for FinSequence of REAL,
  p for Prime;

theorem Th1:
  i1 divides i2 & i1 divides i3 implies i1 divides i2-i3
proof
  assume that
A1: i1 divides i2 and
A2: i1 divides i3;
  consider i4 such that
A3: i2=i1*i4 by A1;
  consider i5 such that
A4: i3=i1*i5 by A2;
  i2-i3=i1*(i4-i5) by A3,A4;
  hence thesis;
end;
