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 (R1) (R10) implies (1.S)" * a =*=> a
  proof
    assume
A1: S is (R1) (R10);
    (1.S)"*a ==> 1.S*a & 1.S*a ==> a by A1,ThI2;
    hence (1.S)" * a =*=> a by Lem3;
  end;
