reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th26:
  for a1,n1,a2,n2 being Integer
  for x being Integer st x solves_CRT a1,n1,a2,n2
  for k being Integer holds x + k*n1*n2 solves_CRT a1,n1,a2,n2
  proof
    let a1,n1,a2,n2 be Integer;
    let x be Integer such that
A1: x solves_CRT a1,n1,a2,n2;
    let k be Integer;
    set y = x + k*n1*n2;
    k*n2*n1,0 are_congruent_mod n1;
    then y,a1+0 are_congruent_mod n1 by A1,INT_1:16;
    hence y,a1 are_congruent_mod n1;
    k*n1*n2,0 are_congruent_mod n2;
    then y,a2+0 are_congruent_mod n2 by A1,INT_1:16;
    hence y,a2 are_congruent_mod n2;
  end;
