We define the notion of inductive invariants for

continuous dynamical systems and use it

to present inference rules for

safety verification of polynomial continuous

dynamical systems.

We present two different sound and complete inference

rules, but neither of these rules can be effectively applied.

We then present several simpler and practical

inference rules that are sound and relatively complete

for different classes of inductive invariants.

The simpler inference rules can be effectively checked when

all involved sets are semi-algebraic.