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.

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