proposition: Lemma Rsqr_u_epsilon : forall (eps : posreal) (t : R), Rsqr (u eps t) = (Rsqr (u0 t) + Rsqr eps)%R.
proof: Proof. intros; apply sqrt_inj; [ apply Rle_0_sqr | apply Rplus_le_le_0_compat; apply Rle_0_sqr | rewrite sqrt_Rsqr; [ unfold u0 in |- *; rewrite Rsqr_sqrt; [ unfold u in |- *; reflexivity | apply Rplus_le_le_0_compat; apply Rle_0_sqr ] | apply (u_pos eps t) ] ]. Qed.
imports: Reals trajectory_const rrho trajectory_def constants