reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;
reserve M,M1,M2 for Matrix of D;
reserve f for FinSequence of D;
reserve i,j,i1,j1 for Nat;
reserve k for Nat, G for Matrix of D;
reserve x,y,x1,x2,y1,y2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  s,s2 for FinSequence,
  a,b,c,d for Element of D,
  q,r for FinSequence of D,
  a9,b9 for Element of D;

theorem Th66:
  i in Seg width G & width G > 1 & n in dom G & m in Seg width
  DelCol(G,i) implies DelCol(G,i)*(n,m)=Del(Line(G,n),i).m
proof
  assume that
A1: i in Seg width G & width G > 1 & n in dom G and
A2: m in Seg width (DelCol(G,i));
  thus DelCol(G,i)*(n,m) = Line(DelCol(G,i),n).m by A2,Def7
    .= Del(Line(G,n),i).m by A1,Th62;
end;
