reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;

theorem
  for n being Nat st n >= 1 holds 1*n <> 0*n
proof
  let n be Nat;
  assume n >= 1;
  then
A1: 1 in Seg n by FINSEQ_1:1;
  assume
A2: 1*n = 0*n;
  1*n = n|->1 & (n|->0).1 = 0 by A1,FUNCOP_1:7;
  hence contradiction by A2,A1,FUNCOP_1:7;
end;
