theorem Th122: :: MATRIX13:122

for m, n being Nat
for K being Field
for M being Matrix of m,n,K
for U being Subset of (n -VectSp_over K) st U c= lines M holds
ex P being finite without_zero Subset of NAT st
( P c= Seg m & lines (Segm (M,P,(Seg n))) = U & Segm (M,P,(Seg n)) is without_repeated_line )