reserve X for BCI-algebra;
reserve x,y,z for Element of X;
reserve i,j,k,l,m,n for Nat;
reserve f,g for sequence of the carrier of X;

theorem
  for X being BCK-algebra of i,j,m,n st i = min(i,j,m,n) holds ( i = n &
  i = m implies X is BCK-algebra of i,i,i,i )
proof
  let X be BCK-algebra of i,j,m,n;
  assume
A1: i = min(i,j,m,n);
  assume
A2: i = n & i = m;
  then for x,y being Element of X holds Polynom (i,i,x,y) = Polynom (i,j,y,x)
  by Def3;
  then
A3: X is BCK-algebra of i,i,i,j by Def3;
  i = min(i,i,i,j) by A1,A2;
  hence thesis by A3,Th27;
end;
