Section Schellinx_observation.
(* This is an observation purely about cut-free CLL  One cannot get a cut-free CLL proof of Γ ⊢ ∅ unless ⟘ or 𝟘 or a negation occurs in Γ *)
Let schellinx_rec Γ Δ :
Γ ⊢c Δ
-> Δ = ∅
-> exists f, In f Γ /\ cll_has_bot_zero_neg f.

Lemma cll_ill_soundness Γ A :
⟦Γ⟧ ⊢c [A]::∅
-> Γ ⊢i A
\/ ill_has_bot A
\/ exists f, In f Γ /\ ill_has_bot f.