reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;
reserve z for Complex;

theorem Th32:
  i,j are_congruent_mod j implies j divides i
  proof
    assume i,j are_congruent_mod j;
    then consider k being Integer such that
A1: i = k * j + j by NAT_6:9;
    i = j * (k+1) by A1;
    hence j divides i;
  end;
