1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground/relocation/pr_isu_uni.ma".
16 include "ground/relocation/pr_after_uni.ma".
18 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
20 (* Constructions with pr_isu ************************************************)
22 (*** after_isid_isuni *)
23 lemma pr_after_isu_isi_next:
24 ∀f1,f2. 𝐈❨f2❩ → 𝐔❨f1❩ → f1 ⊚ ↑f2 ≘ ↑f1.
26 elim (pr_isu_inv_uni … H) -H #h #H
27 /5 width=7 by pr_after_uni_isi_next, pr_after_eq_repl_back, pr_after_eq_repl_back_sn, pr_eq_next/
30 (*** after_uni_next2 *)
31 lemma pr_after_isu_next_sn:
32 ∀f2. 𝐔❨f2❩ → ∀f1,f. ↑f2 ⊚ f1 ≘ f → f2 ⊚ ↑f1 ≘ f.
34 elim (pr_isu_inv_uni … H) -H #h #H
35 /5 width=7 by pr_after_uni_next_sn, pr_after_eq_repl_fwd_sn, pr_after_eq_repl_back_sn, pr_eq_next/