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 k >= max(i,j,m,n) holds X is
  BCK-algebra of k,k,k,k
proof
  let X be BCK-algebra of i,j,m,n;
  assume
A1: k >= max(i,j,m,n);
  max(i,j,m,n) >= n by Th26;
  then k - n is Element of NAT by A1,NAT_1:21,XXREAL_0:2;
  then consider t1 being Element of NAT such that
A2: t1=k-n;
  max(i,j,m,n) >= j by Th26;
  then k - j is Element of NAT by A1,NAT_1:21,XXREAL_0:2;
  then consider t being Element of NAT such that
A3: t=k-j;
  X is BCK-algebra of n,j,m,n by Th22;
  then X is BCK-algebra of n,j,j,n by Th21;
  then X is BCK-algebra of n+t1,j,j,n+t1 by Th17;
  then X is BCK-algebra of k,j+t,j+t,k by A2,Th18;
  hence thesis by A3;
end;
