for f1, f2, f3, g1, g2, g3 being PartFunc of REAL,REAL
for t0 being Real st f1 is_differentiable_in t0 & f2 is_differentiable_in t0 & f3 is_differentiable_in t0 & g1 is_differentiable_in t0 & g2 is_differentiable_in t0 & g3 is_differentiable_in t0 holds
VFuncdiff (((f2 (#) g3) - (f3 (#) g2)),((f3 (#) g1) - (f1 (#) g3)),((f1 (#) g2) - (f2 (#) g1)),t0) = |[(((f2 . t0) * (diff (g3,t0))) - ((f3 . t0) * (diff (g2,t0)))),(((f3 . t0) * (diff (g1,t0))) - ((f1 . t0) * (diff (g3,t0)))),(((f1 . t0) * (diff (g2,t0))) - ((f2 . t0) * (diff (g1,t0))))]| + |[(((diff (f2,t0)) * (g3 . t0)) - ((diff (f3,t0)) * (g2 . t0))),(((diff (f3,t0)) * (g1 . t0)) - ((diff (f1,t0)) * (g3 . t0))),(((diff (f1,t0)) * (g2 . t0)) - ((diff (f2,t0)) * (g1 . t0)))]|