Section ContainsAutomation.
End ContainsAutomation.
End FullFOL.
Definition tmap {S1 S2 : Signature} (f : @form S1 -> @form S2) (T : @theory S1) : @theory S2 :=
fun phi => exists psi, T psi /\ f psi = phi.

Lemma tmap_contains_L {S1 S2 : Signature} (f : @form S1 -> @form S2) T A :
contains_L A (tmap f T) -> exists B, A = List.map f B /\ contains_L B T.