let D be non empty set ; :: thesis: for A being Matrix of D
for P, Q being finite without_zero Subset of NAT holds
not ( [:P,Q:] c= Indices A & ( card P = 0 implies card Q = 0 ) & ( card Q = 0 implies card P = 0 ) & not (Segm (A,P,Q)) @ = Segm ((A @),Q,P) )
let A be Matrix of D; :: thesis: for P, Q being finite without_zero Subset of NAT holds
not ( [:P,Q:] c= Indices A & ( card P = 0 implies card Q = 0 ) & ( card Q = 0 implies card P = 0 ) & not (Segm (A,P,Q)) @ = Segm ((A @),Q,P) )
let P, Q be finite without_zero Subset of NAT; :: thesis: not ( [:P,Q:] c= Indices A & ( card P = 0 implies card Q = 0 ) & ( card Q = 0 implies card P = 0 ) & not (Segm (A,P,Q)) @ = Segm ((A @),Q,P) )
( rng (Sgm Q) = Q & rng (Sgm P) = P ) by FINSEQ_1:def 14;
hence not ( [:P,Q:] c= Indices A & ( card P = 0 implies card Q = 0 ) & ( card Q = 0 implies card P = 0 ) & not (Segm (A,P,Q)) @ = Segm ((A @),Q,P) ) by Th18; :: thesis: verum