theorem Th1:
i <= j implies (0*j) | i = 0*i
proof
   assume A1: i <= j;
A2:((0*i)^(0*((j-'i)))) | (len(0*i)) = 0*i by FINSEQ_5:23;
    i+(j-'i) = (i+j)-'i by A1,Lm2;
   then i+(j-'i) = i+j -i by XREAL_0:def 2;
   then (0*i)^(0*((j-'i))) = 0*j by FINSEQ_2:123;
   hence thesis by A2,CARD_1:def 7;
end;
