theorem Th18: :: MATRIX13:18

for D being non empty set
for m, n being Nat
for A being Matrix of D
for nt being Element of n -tuples_on NAT
for mt being Element of m -tuples_on NAT holds
not ( [:(rng nt),(rng mt):] c= Indices A & ( n = 0 implies m = 0 ) & ( m = 0 implies n = 0 ) & not (Segm (A,nt,mt)) @ = Segm ((A @),mt,nt) )