
theorem RMI:
  for a,b be Nat, c,d be non zero Nat holds
    a mod (c*d) = b mod (c*d) implies a mod c = b mod c
  proof let a,b be Nat, c,d be non zero Nat;
    assume a mod (c*d) = b mod (c*d); then
    a mod (c*d) mod c = b mod c by RADIX_1:3;
    hence thesis by RADIX_1:3;
  end;
