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 Th25:
  i = min(i,j,m,n) implies i<=j & i<=m & i<=n
proof
A1: min(m,n)<= n by XXREAL_0:17;
  assume i = min(i,j,m,n);
  then
A2: i<= min(i,j) & i<= min(m,n) by XXREAL_0:17;
  min(i,j) <= j & min(m,n)<= m by XXREAL_0:17;
  hence thesis by A2,A1,XXREAL_0:2;
end;
