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 (R11) (R14) implies a * (b * (a * b)") =*=> 1.S
  proof
    assume
A1: S is (R11) (R14);
    a * (b * (a * b)") ==> a*a" & a*a" ==> 1.S by A1,ThI3;
    hence a * (b * (a * b)") =*=> 1.S by Lem3;
  end;
