theorem Th40: :: CHAIN_1:43

for d being non zero Nat
for G being Grating of d
for A being Subset of (REAL d) holds
( A in cells (1,G) iff ex l, r being Element of REAL d ex i0 being Element of Seg d st
( A = cell (l,r) & ( l . i0 < r . i0 or ( d = 1 & r . i0 < l . i0 ) ) & [(l . i0),(r . i0)] is Gap of G . i0 & ( for i being Element of Seg d st i <> i0 holds
( l . i = r . i & l . i in G . i ) ) ) )