reserve i,n,m for Nat;

theorem Th11:
for IT be Function of REAL m,REAL n st IT is additive holds IT.(0*m) = 0*n
proof
   let IT be Function of REAL m,REAL n;
   assume A1: IT is additive;
   IT.(0*m) = IT.(0*m + 0*m) by RVSUM_1:16; then
   IT.(0*m) = IT.(0*m) + IT.(0*m) by A1; then
   0*n = IT.(0*m) + IT.(0*m) -(IT.(0*m)) by RVSUM_1:37;
   hence 0*n = IT.(0*m) by RVSUM_1:42;
end;
