reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;

theorem
  abs 0*n = n |-> (0 qua Real)
proof
  reconsider m=n as Element of NAT by ORDINAL1:def 12;
  thus abs 0*n = m |-> absreal.(0 qua Real) by FINSEQOP:16
    .= n |-> |.0 .| by Def2
    .= n |-> 0 by ABSVALUE:2;
end;
