proposition: Lemma itv_partitionxx a s : itv_partition a a s -> s = [::].
proof: Proof. case: s => //= h t [/= /andP[ah /lt_path_min/allP ht] /eqP hta]. suff : h < a by move/lt_trans => /(_ _ ah); rewrite ltxx. apply/ht; rewrite -hta. by have := mem_last h t; rewrite inE hta lt_eqF. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum finmap) mathcomp(matrix interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) ereal reals signed topology prodnormedzmodule normedtype derive sequences real_interval HB(structures)