Definition semax_equiv {CS: compspecs} {Espec: OracleKind} c1 c2: Prop := forall Delta P Q, semax Delta P c1 Q <-> semax Delta P c2 Q.

Lemma semax_equiv_trans: forall {CS: compspecs} {Espec: OracleKind} c1 c2 c3, semax_equiv c1 c2 -> semax_equiv c2 c3 -> semax_equiv c1 c3.