+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/rajuststar_5.ma".
-include "basic_2/substitution/fpa.ma".
-
-(* MULTIPLE AJUSTMENT *******************************************************)
-
-definition fpas: bool → bi_relation lenv term ≝ λs. bi_TC … (fpa s).
-
-interpretation
- "multiple ajustment (restricted closure)"
- 'RAjustStar L1 T1 s L2 T2 = (fpas s L1 T1 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma fpas_ind: ∀L1,T1,s. ∀R:relation2 …. R L1 T1 →
- (∀L,L2,T,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳[s] ⦃L2, T2⦄ → R L T → R L2 T2) →
- ∀L2,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ → R L2 T2.
-#L1 #T1 #s #R #IH1 #IH2 #L2 #T2 #H
-@(bi_TC_star_ind … IH1 IH2 L2 T2 H) //
-qed-.
-
-lemma fpas_ind_dx: ∀L2,T2,s. ∀R:relation2 …. R L2 T2 →
- (∀L1,L,T1,T. ⦃L1, T1⦄ ⇳[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ → R L T → R L1 T1) →
- ∀L1,T1. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ → R L1 T1.
-#L2 #T2 #s #R #IH1 #IH2 #L1 #T1 #H
-@(bi_TC_star_ind_dx … IH1 IH2 L1 T1 H) //
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma fpas_refl: ∀s. bi_reflexive … (fpas s).
-/2 width=1 by bi_inj/ qed.
-
-lemma fpas_sym: ∀s. bi_symmetric … (fpas s).
-/3 width=1 by fpa_sym, bi_TC_symmetric/ qed-.
-
-lemma fpa_fpas: ∀L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L2, T2⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
-/2 width=1 by bi_inj/ qed.
-
-lemma fpas_strap1: ∀L1,L,L2,T1,T,T2,s. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳[s] ⦃L2, T2⦄ →
- ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
-/2 width=4 by bi_step/ qed-.
-
-lemma fpas_strap2: ∀L1,L,L2,T1,T,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ →
- ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
-/2 width=4 by bi_TC_strap/ qed-.