Section KSoundness.
Context {Σ_funcs : funcs_signature}.
Context {Σ_preds : preds_signature}.
Context {ff : falsity_flag}.
Ltac clean_ksoundness :=
match goal with
| [ H : ?x = ?x -> _ |- _ ] => specialize (H eq_refl)
| [ H : (?A -> ?B), H2 : (?A -> ?B) -> _ |- _] => specialize (H2 H)
end.

Lemma ksoundness A (phi : form) :
A ⊢I phi -> kvalid_ctx A phi.