Hint Resolvegt_not_eqeq_not_lt : ordered_type. Hint Immediateeq_ltlt_eqle_eqeq_leneq_eqeq_neq : ordered_type. Hint Resolveeq_not_gtlt_antirefllt_not_gt : ordered_type.
Hint Resolveeqk_transeqke_transeqk_refleqke_refl : ordered_type. Hint Resolveltk_transltk_not_eqkltk_not_eqke : ordered_type. Hint Immediateeqk_symeqke_sym : ordered_type.
Hint Unfoldeqkeqkeltk : ordered_type. Hint Extern 2 (eqke ?a ?b) => split : ordered_type. Hint Resolveeqk_transeqke_transeqk_refleqke_refl : ordered_type. Hint Resolveltk_transltk_not_eqkltk_not_eqke : ordered_type. Hint Immediateeqk_symeqke_sym : ordered_type. Hint Resolveeqk_not_ltk : ordered_type. Hint Immediateltk_eqkeqk_ltk : ordered_type. Hint ResolveInA_eqke_eqk : ordered_type. Hint UnfoldMapsToIn : ordered_type. Hint ImmediateInf_eq : ordered_type. Hint ResolveInf_lt : ordered_type. Hint ResolveSort_Inf_NotIn : ordered_type. Hint ResolveIn_inv_2In_inv_3 : ordered_type.