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;
