let i, n be Nat; :: thesis: for K being Field
for A being Matrix of K
for nt being Element of n -tuples_on NAT st i in Seg n holds
Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i))

let K be Field; :: thesis: for A being Matrix of K
for nt being Element of n -tuples_on NAT st i in Seg n holds
Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i))

let A be Matrix of K; :: thesis: for nt being Element of n -tuples_on NAT st i in Seg n holds
Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i))

let nt be Element of n -tuples_on NAT; :: thesis: ( i in Seg n implies Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i)) )
set S = Seg ();
A1: rng (Sgm (Seg ())) = Seg () by FINSEQ_1:def 13;
len (Line (A,(nt . i))) = width A by MATRIX_0:def 7;
then A2: dom (Line (A,(nt . i))) = Seg () by FINSEQ_1:def 3;
Sgm (Seg ()) = idseq () by FINSEQ_3:48;
then A3: (Line (A,(nt . i))) * (Sgm (Seg ())) = Line (A,(nt . i)) by ;
assume i in Seg n ; :: thesis: Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i))
hence Line ((Segm (A,nt,(Sgm (Seg ())))),i) = Line (A,(nt . i)) by ; :: thesis: verum