reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;
reserve i,j,k for Element of ARS_01;
reserve l,m,n for Element of ARS_02;
reserve A for set;
reserve
  S for Group-like quasi_total partial invariant non empty non-empty TRSStr;
reserve a,b,c for Element of S;
reserve S for Group-like quasi_total partial non empty non-empty TRSStr;
reserve a,b,c for Element of S;
reserve
  S for Group-like quasi_total partial invariant non empty non-empty TRSStr,
  a,b,c for Element of S;

theorem
  S is (R4) (R14) implies (a * b)" <<>> b" * a"
  proof
    assume
A1: S is (R4) (R14);
    take b"*(b*(a*b)");
    thus b"*(b*(a*b)") =*=> (a * b)" by A1,Th2;
    (b*(a*b)") ==> a" by A1;
    hence b"*(b*(a*b)") =*=> b" * a" by Th2,ThI3;
  end;
