Proof with trivial.
intros; unfold conflict in |- *; case (Rle_dec (Die T T) ConflictRange);
intro...
cut (0 <= T)%R...
intro; generalize (no_conflict_gt_max_t T H0 H); intro; cut (e T = Die T T)...
intro; rewrite H2 in H1;
elim
(Rlt_irrefl (Die T T) (Rle_lt_trans (Die T T) ConflictRange (Die T T) r H1))...
left; apply Rlt_le_trans with MinT...
apply MinT_is_pos...
apply (cond_1 T)...
Qed.

Theorem no_conflict_lt_min :
let MinDistance := (2 * r_vi * sin (rho_vi * (T / 2)) - ConflictRange)%R in
(0 <= rho_vi * T)%R ->
(rho_vi * T < 2)%R -> (l < MinDistance)%R -> conflict T = false.