reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;
reserve J for Nat;
reserve n for Nat;
reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;

theorem
  Union <*X,Y,Z*> = X \/ Y \/ Z & meet <*X,Y,Z*> = X /\ Y /\ Z
proof
A1: union ({X,Y} \/ {Z}) = union {X,Y} \/ union {Z} & union {X,Y} = X \/ Y
  by ZFMISC_1:75,78;
A2: union {Z} = Z by ZFMISC_1:25;
A3: {X,Y} \/ {Z} = {X,Y,Z} by ENUMSET1:3;
  thus Union <*X,Y,Z*> = union rng <*X,Y,Z*>
    .= X \/ Y \/ Z by A1,A2,A3,FINSEQ_2:128;
A4: meet {Z} = Z by SETFAM_1:10;
  meet ({X,Y} \/ {Z}) = meet {X,Y} /\ meet {Z} & meet {X,Y} = X /\ Y by
SETFAM_1:9,11;
  hence thesis by A4,A3,FINSEQ_2:128;
end;
