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;

theorem ThA:
  for S being non empty non-empty UAStr st S is Group-like
  holds
    1 is OperSymbol of S & 2 is OperSymbol of S & 3 is OperSymbol of S
    proof
      let S be non empty non-empty UAStr;
      assume
A0:   Seg 3 c= dom the charact of S;
      1 in Seg 3 & 2 in Seg 3 & 3 in Seg 3 by FINSEQ_3:1,ENUMSET1:def 1;
      hence thesis by A0;
    end;
