theorem Th30: :: CHAIN_1:33

for k being Nat
for d being non zero Nat
for l, r being Element of REAL d
for G being Grating of d st k <= d holds
( cell (l,r) in cells (k,G) iff ( ex X being Subset of (Seg d) st
( card X = k & ( for i being Element of Seg d holds
( ( i in X & l . i < r . i & [(l . i),(r . i)] is Gap of G . i ) or ( not i in X & l . i = r . i & l . i in G . i ) ) ) ) or ( k = d & ( for i being Element of Seg d holds
( r . i < l . i & [(l . i),(r . i)] is Gap of G . i ) ) ) ) )