theorem Th75: :: MATRIX13:75

for n being Nat
for K being Field
for nt1, nt2 being Element of n -tuples_on NAT
for M being Matrix of K st [:(rng nt1),(rng nt2):] c= Indices M & Det (Segm (M,nt1,nt2)) <> 0. K holds
ex P1, P2 being finite without_zero Subset of NAT st
( P1 = rng nt1 & P2 = rng nt2 & card P1 = card P2 & card P1 = n & Det (EqSegm (M,P1,P2)) <> 0. K )