+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ➡ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
- non associative with precedence 45
- for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
-
-include "basic_2/reducibility/tpr.ma".
-
-(* CONTEXT-FREE PARALLEL REDUCTION ON CLOSURES ******************************)
-
-definition fpr: bi_relation lenv term ≝
- λL1,T1,L2,T2. |L1| = |L2| ∧ L1 @@ T1 ➡ L2 @@ T2.
-
-interpretation
- "context-free parallel reduction (closure)"
- 'FocalizedPRed L1 T1 L2 T2 = (fpr L1 T1 L2 T2).
-
-(* Basic properties *********************************************************)
-
-lemma fpr_refl: bi_reflexive … fpr.
-/2 width=1/ qed.
-
-lemma fpr_shift: ∀I1,I2,L1,L2,V1,V2,T1,T2.
- ⦃L1, -ⓑ{I1}V1.T1⦄ ➡ ⦃L2, -ⓑ{I2}V2.T2⦄ →
- ⦃L1.ⓑ{I1}V1, T1⦄ ➡ ⦃L2.ⓑ{I2}V2, T2⦄.
-#I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 * #HL12 #HT12
-@conj // normalize // (**) (* explicit constructor *)
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma fpr_inv_atom1: ∀L2,T1,T2. ⦃⋆, T1⦄ ➡ ⦃L2, T2⦄ → T1 ➡ T2 ∧ L2 = ⋆.
-#L2 #T1 #T2 * #H
-lapply (length_inv_zero_sn … H) -H #H destruct /2 width=1/
-qed-.
-
-lemma fpr_inv_atom3: ∀L1,T1,T2. ⦃L1,T1⦄ ➡ ⦃⋆,T2⦄ → T1 ➡ T2 ∧ L1 = ⋆.
-#L1 #T1 #T2 * #H
-lapply (length_inv_zero_dx … H) -H #H destruct /2 width=1/
-qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma fpr_fwd_pair1: ∀I1,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I1}V1, T1⦄ ➡ ⦃L2, T2⦄ →
- ∃∃I2,K2,V2. ⦃K1, -ⓑ{I1}V1.T1⦄ ➡ ⦃K2, -ⓑ{I2}V2.T2⦄ &
- L2 = K2.ⓑ{I2}V2.
-#I1 #K1 #L2 #V1 #T1 #T2 * #H
-elim (length_inv_pos_sn … H) -H #I2 #K2 #V2 #HK12 #H destruct /3 width=5/
-qed-.
-
-lemma fpr_fwd_pair3: ∀I2,L1,K2,V2,T1,T2. ⦃L1, T1⦄ ➡ ⦃K2.ⓑ{I2}V2, T2⦄ →
- ∃∃I1,K1,V1. ⦃K1, -ⓑ{I1}V1.T1⦄ ➡ ⦃K2, -ⓑ{I2}V2.T2⦄ &
- L1 = K1.ⓑ{I1}V1.
-#I2 #L1 #K2 #V2 #T1 #T2 * #H
-elim (length_inv_pos_dx … H) -H #I1 #K1 #V1 #HK12 #H destruct /3 width=5/
-qed-.