proposition: Lemma ZEven_pow_le (r : R) (n : nat) : Z.Even (Z_of_nat n) -> (0 <= r ^ n)%R.
proof: Proof. move=> [k Hk]. rewrite pow_Rabs_sign; case: Rle_bool_spec =>[_|Hr]. rewrite powerRZ_R1 Rmult_1_l. apply: pow_le. exact: Rabs_pos. rewrite Hk. apply: Rmult_le_pos_pos; first exact: powerRZ_1_even. by apply: pow_le; exact: Rabs_pos. Qed.
imports: Coq(ZArith Psatz Reals) Flocq(Raux) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Stdlib MathComp Coquelicot Xreal Interval Basic Xreal_derive Interval_compl Datatypes Taylor_poly Basic_rec Bound