Section S_ill_cll_restr.
Notation "Γ '⊢i' A" := (S_ill_restr Γ A) (at level 70).
Notation "Γ '⊢c' Δ" := (S_cll_restr Γ Δ) (at level 70).
Hint Resolve Permutation_map : core.
Let cll_ill_empty_rec Γ Δ : Γ ⊢c Δ -> Δ <> ∅.
Let cll_ill_empty Γ : ~ Γ ⊢c ∅.
Hint Resolve S_ill_cll_restr S_cll_ill_restr : core.

Theorem S_ill_cll_restr_equiv Γ A : Γ ⊢i A <-> ⟦Γ⟧ ⊢c [A]::∅.