reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th1:
  l = min(i,j) implies Seg i /\ Seg j = Seg l
proof
  i <= j or j <= i;
  then i <= j & Seg i /\ Seg j = Seg i or j <= i & Seg i /\ Seg j = Seg j by
FINSEQ_1:7;
  hence thesis by XXREAL_0:def 9;
end;
