reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  n <> 0 & k mod n = 0 & l < n implies k + l mod n = l
proof
A0: k is Nat & n is Nat & l is Nat by TARSKI:1;
  assume that
A1: n <> 0 and
A2: k mod n = 0 and
A3: l < n;
  ex t being Nat st k = n * t + 0 & 0 < n by A1,A2,Def2;
  hence thesis by A0,A3,Def2;
end;
