proposition: Lemma Math_prop_x_a_PI2 : forall (a l : R) (T : TimeT), (MinBeta <= a)%R -> (a <= PI / 2)%R -> (0 <= l)%R -> (r_V * sin (rho_V * T) - l * cos MinBeta <= r_V * sin (rho_V * T) - l * cos a)%R.
proof: Proof. intros; unfold Rminus in |- *; apply Rplus_le_compat_l; apply Ropp_ge_le_contravar; apply Rle_ge; apply Rmult_le_compat_l; [ assumption | apply cos_decr_1; [ left; apply MinBeta_pos | apply Rle_trans with a; [ assumption | left; apply Rle_lt_trans with (PI / 2)%R; [ assumption | apply PI2_Rlt_PI ] ] | left; apply Rlt_le_trans with MinBeta; [ apply MinBeta_pos | assumption ] | left; apply Rle_lt_trans with (PI / 2)%R; [ assumption | apply PI2_Rlt_PI ] | assumption ] ]. Qed.
imports: Reals trajectory_const rrho constants Omega