+++ /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 "ground/relocation/gr_tls.ma".
-include "ground/relocation/gr_nat.ma".
-include "ground/relocation/gr_isi_uni.ma".
-include "ground/relocation/gr_after_isi.ma".
-
-(* RELATIONAL COMPOSITION FOR GENERIC RELOCATION MAPS ***********************)
-
-(* Constructions with gr_nat and gr_uni *************************************)
-
-(*** after_uni_dx *)
-lemma gr_after_nat_uni (l2) (l1):
- ∀f2. @↑❪l1, f2❫ ≘ l2 →
- ∀f. f2 ⊚ 𝐮❨l1❩ ≘ f → 𝐮❨l2❩ ⊚ ⫰*[l2] f2 ≘ f.
-#l2 @(nat_ind_succ … l2) -l2
-[ #l1 #f2 #Hf2 #f #Hf
- elim (gr_nat_inv_zero_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct
- lapply (gr_after_isi_inv_dx … Hf ?) -Hf
- /3 width=3 by gr_after_isi_sn, gr_after_eq_repl_back/
-| #l2 #IH #l1 #f2 #Hf2 #f #Hf
- elim (gr_nat_inv_succ_dx … Hf2) -Hf2 [1,3: * |*: // ]
- [ #g2 #k1 #Hg2 #H1 #H2 destruct
- elim (gr_after_inv_push_next … Hf) -Hf [ |*: // ] #g #Hg #H destruct
- <gr_tls_swap /3 width=5 by gr_after_next/
- | #g2 #Hg2 #H2 destruct
- elim (gr_after_inv_next_sn … Hf) -Hf [ |*: // ] #g #Hg #H destruct
- <gr_tls_swap /3 width=5 by gr_after_next/
- ]
-]
-qed.
-
-(*** after_uni_sn *)
-lemma gr_nat_after_uni_tls (l2) (l1):
- ∀f2. @↑❪l1, f2❫ ≘ l2 →
- ∀f. 𝐮❨l2❩ ⊚ ⫰*[l2] f2 ≘ f → f2 ⊚ 𝐮❨l1❩ ≘ f.
-#l2 @(nat_ind_succ … l2) -l2
-[ #l1 #f2 #Hf2 #f #Hf
- elim (gr_nat_inv_zero_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct
- lapply (gr_after_isi_inv_sn … Hf ?) -Hf
- /3 width=3 by gr_after_isi_dx, gr_after_eq_repl_back/
-| #l2 #IH #l1 #f2 #Hf2 #f #Hf
- elim (gr_after_inv_next_sn … Hf) -Hf [2,3: // ] #g #Hg #H destruct
- elim (gr_nat_inv_succ_dx … Hf2) -Hf2 [1,3: * |*: // ]
- [ #g2 #k1 #Hg2 #H1 #H2 destruct /3 width=7 by gr_after_push/
- | #g2 #Hg2 #H2 destruct /3 width=5 by gr_after_next/
- ]
-]
-qed-.