theorem Th7: :: COMBGRAS:7

for n being Nat
for a, b, c being set st card a = n - 1 & card b = n - 1 & card c = n - 1 & card (a /\ b) = n - 2 & card (a /\ c) = n - 2 & card (b /\ c) = n - 2 & 2 <= n holds
( ( not 3 <= n or ( card ((a /\ b) /\ c) = n - 2 & card ((a \/ b) \/ c) = n + 1 ) or ( card ((a /\ b) /\ c) = n - 3 & card ((a \/ b) \/ c) = n ) ) & ( n = 2 implies ( card ((a /\ b) /\ c) = n - 2 & card ((a \/ b) \/ c) = n + 1 ) ) )