Proof with trivial.
intro; rewrite <- d_distance; rewrite distance_sym; rewrite <- R_distance...
cut (0 <= T)%R...
intro;
generalize
(asymptotic_increase_tau (measure2state intr 0) (measure2state (tr evad) 0)
0 0 T H H0); intro...
repeat rewrite Rplus_0_l in H1...
left; apply Rlt_le_trans with MinT...
apply MinT_is_pos...
apply (cond_1 T)...
Qed.

Lemma R_T_d_diff_0 :
h (tr evad) = V ->
(0 < l intr evad T)%R ->
(d intr evad <= RR (measure2state intr 0) (measure2state (tr evad) 0) T)%R ->
(cos (beta intr evad T + thetat intr 0) <= cos (beta intr evad T))%R.