reserve p,q for Point of TOP-REAL 2,
  i,i1,i2,j,j1,j2,k for Nat,
  r,s for Real,
  G for Matrix of TOP-REAL 2;

theorem Th8:
  G is X_equal-in-line & 1 <= i & i < len G & 1 <= j & j <= width G
  implies v_strip(G,i) = { |[r,s]| : G*(i,j)`1 <= r & r <= G*(i+1,j)`1 }
proof
  assume that
A1: G is X_equal-in-line and
A2: 1 <= i and
A3: i < len G and
A4: 1 <= j and
A5: j <= width G;
A6: 1 <= i+1 by A2,NAT_1:13;
A7: i+1 <= len G by A3,NAT_1:13;
A8: G*(i,j)`1 = G*(i,1)`1 by A1,A2,A3,A4,A5,Th2;
  G*(i+1,j)`1 = G*(i+1,1)`1 by A1,A4,A5,A6,A7,Th2;
  hence thesis by A2,A3,A8,Def1;
end;
