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 Th67:
  p in q & r <> p & r <> q & s <> p & s <> q implies (T,p,q)incl.(r,s) = [r,s]
  proof assume
A1: p in q & r <> p & r <> q & s <> p & s <> q;
    set X = dom T;
    set i = id X;
    set f = Swap(i,p,q);
    set h = [:f,f:];
    set Y = (succ q)\p;
    thus (T,p,q)incl.(r,s) = [f.r,f.s] by A1,Th63
    .= [i.r,f.s] by A1,Th33 .= [i.r,i.s] by A1,Th33
    .= [r,i.s]
    .= [r,s];
  end;
