One way to get around this is this: For reducible constraints, we relax the condition on the right invertibility of Δ f into this one: Any smooth function that vanishes at the zeros of f is the fiberwise contraction of f with (a non-unique) smooth section of a V ¯ ¯ -vector bundle where V ¯ ¯ is the dual vector space to the constraint vector space V. This is called the regularity condition.