include "static_2/relocation/lex.ma".
include "basic_2/notation/relations/pconveta_4.ma".
-include "basic_2/rt_conversion/cpce.ma".
+include "basic_2/rt_conversion/cpce_ext.ma".
(* PARALLEL ETA-CONVERSION FOR FULL LOCAL ENVIRONMENTS **********************)
"parallel eta-conversion on all entries (local environment)"
'PConvEta h G L1 L2 = (lpce h G L1 L2).
+(* Basic properties *********************************************************)
+
+lemma lpce_bind (h) (G):
+ ∀K1,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 →
+ ∀I1,I2. ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 → ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] K2.ⓘ{I2}.
+/2 width=1 by lex_bind/ qed.
+
(* Advanced properties ******************************************************)
lemma lpce_pair (h) (G):
∀L2. ⦃G,⋆⦄ ⊢ ⬌η[h] L2 → L2 = ⋆.
/2 width=2 by lex_inv_atom_sn/ qed-.
+lemma lpce_inv_bind_sn (h) (G):
+ ∀I1,L2,K1. ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] L2 →
+ ∃∃I2,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L2 = K2.ⓘ{I2}.
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
lemma lpce_inv_atom_dx (h) (G):
∀L1. ⦃G,L1⦄ ⊢ ⬌η[h] ⋆ → L1 = ⋆.
/2 width=2 by lex_inv_atom_dx/ qed-.
+lemma lpce_inv_bind_dx (h) (G):
+ ∀I2,L1,K2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓘ{I2} →
+ ∃∃I1,K1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L1 = K1.ⓘ{I1}.
+/2 width=1 by lex_inv_bind_dx/ qed-.
+
(* Advanced inversion lemmas ************************************************)
lemma lpce_inv_unit_sn (h) (G):