reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;
reserve O for connected non empty Poset;
reserve R,Q for array of O;
reserve T for non empty array of O;
reserve p,q,r,s for Element of dom T;

theorem Th60:
  (succ q)\p c= dom T
  proof
    let x be object;
      reconsider xx=x as set by TARSKI:1;
assume
A1: x in (succ q)\p;
A2: p c= xx & xx c= q by A1,Th59;
    consider a,b such that
A3: dom T = a\b by Def1;
    q in a & p nin b by A3,XBOOLE_0:def 5; then
    x in a & x nin b by A1,A2,ORDINAL1:12;
    hence thesis by A3,XBOOLE_0:def 5;
  end;
