Section ycngstys.
Unset Standard Proposition Elimination Names.
Variable intr : Trajectory.
Definition thetat : R -> R := theta intr.
Definition Rs (t : R) : R :=
sqrt (Rsqr (xi intr t - xi intr 0) + Rsqr (yi intr t - yi intr 0)).
Axiom
alphas_exists :
{ f : Differential_D2 |
forall t : R,
xi intr t = (Rs t * cos (f t) + xi intr 0)%R /\
yi intr t = (Rs t * sin (f t) + yi intr 0)%R }.
Definition alphas := let (a,_) := alphas_exists in a.
unfold alphas in |- *; case alphas_exists; trivial.
Qed.

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Lemma Rsx : forall t : R, xi intr t = (xi intr 0 + Rs t * cos (alphas t))%R.