theorem
  0*R = i|->0
proof
A1: rng R c= REAL;
  thus 0*R = multreal[;](0,(id REAL)*R) by FUNCOP_1:34
    .= multreal[;](0,R) by A1,RELAT_1:53
    .= i|->0 by Th3,Th8,BINOP_2:2,FINSEQOP:76;
end;
