let D be non empty set ; :: thesis: for i being Nat
for A being Matrix of
for P, Q being finite without_zero Subset of st i in Seg (card P) & Q c= Seg (width A) holds
Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q)
let i be Nat; :: thesis: for A being Matrix of
for P, Q being finite without_zero Subset of st i in Seg (card P) & Q c= Seg (width A) holds
Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q)
let A be Matrix of ; :: thesis: for P, Q being finite without_zero Subset of st i in Seg (card P) & Q c= Seg (width A) holds
Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q)
let P, Q be finite without_zero Subset of ; :: thesis: ( i in Seg (card P) & Q c= Seg (width A) implies Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q) )
assume that
A1: i in Seg (card P) and
A2: Q c= Seg (width A) ; :: thesis: Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q)
rng (Sgm Q) = Q by A2, FINSEQ_1:def 13;
hence Line (Segm A,P,Q),i = (Line A,((Sgm P) . i)) * (Sgm Q) by A1, A2, Th24; :: thesis: verum