∀x ∈ ]a, b[, P > 0

1. not(∃x ∈ ]a, b[, P = 0) P keeps the same sign over ]a, b[ (i.e. as P is continuous, it is the same than P has no zero in ]a, b[)
2. and the disjunction of: (P has a behaviour in a such that P is stricly positive over ]a, b[)
   • (P(a) > 0)
     
   • [P(a) = 0 and P'(a) > 0]
     
   • [P(a) = P'(a) = 0 and P''(a) > 0]
   • ...
   • or [P(a) = P'(a) = ... = P^(d°P-1)(a) = 0 and P^(d°P)(a) > 0]