(* Properties with append for local environments ****************************)
-lemma frees_append_void: ∀f,K,T. K ⊢ 𝐅*⦃T⦄ ≘ f → ⓧ.K ⊢ 𝐅*⦃T⦄ ≘ f.
+lemma frees_append_void: ∀f,K,T. K ⊢ 𝐅+⦃T⦄ ≘ f → ⓧ.K ⊢ 𝐅+⦃T⦄ ≘ f.
#f #K #T #H elim H -f -K -T
[ /2 width=1 by frees_sort/
| #f * /3 width=1 by frees_atom, frees_unit, frees_lref/
(* Inversion lemmas with append for local environments **********************)
-fact frees_inv_append_void_aux: ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f →
- ∀K. L = ⓧ.K → K ⊢ 𝐅*⦃T⦄ ≘ f.
+fact frees_inv_append_void_aux:
+ ∀f,L,T. L ⊢ 𝐅+⦃T⦄ ≘ f →
+ ∀K. L = ⓧ.K → K ⊢ 𝐅+⦃T⦄ ≘ f.
#f #L #T #H elim H -f -L -T
[ /2 width=1 by frees_sort/
| #f #i #_ #K #H
]
qed-.
-lemma frees_inv_append_void: ∀f,K,T. ⓧ.K ⊢ 𝐅*⦃T⦄ ≘ f → K ⊢ 𝐅*⦃T⦄ ≘ f.
+lemma frees_inv_append_void: ∀f,K,T. ⓧ.K ⊢ 𝐅+⦃T⦄ ≘ f → K ⊢ 𝐅+⦃T⦄ ≘ f.
/2 width=3 by frees_inv_append_void_aux/ qed-.