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