Section ycngftys.
Unset Standard Proposition Elimination Names.
Variable intr : Trajectory.
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Definition xi : R -> R := x intr.
Definition yi : R -> R := y intr.
Definition vi : TypeSpeed := h intr.
Definition xP (t : R) : R := (xi t - xi 0)%R.
Definition yP (t : R) : R := (yi t - yi 0)%R.
Definition u (eps : posreal) (t : R) : R :=
sqrt (Rsqr (xP t) + Rsqr (yP t) + Rsqr eps).
Definition u0 (t : R) : R := sqrt (Rsqr (xP t) + Rsqr (yP t)).
unfold xi in |- *; apply (cond_diff (x intr)).
Qed.
unfold yi in |- *; apply (cond_diff (y intr)).
Qed.
unfold xP in |- *.
reg; apply xi_derivable.
Qed.
unfold yP in |- *.
reg; apply yi_derivable.
Qed.

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Lemma d_u : forall eps : posreal, derivable (fun t : R => u eps t).