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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 include "ground/relocation/pr_sle.ma".
16 (* * this should go first *)
17 include "ground/relocation/pr_tl_eq.ma".
19 (* INCLUSION FOR PARTIAL RELOCATION MAPS ************************************)
21 (* Constructions with pr_eq *************************************************)
23 (*** sle_eq_repl_back1 *)
24 corec lemma pr_sle_eq_repl_back_sn:
25 ∀f2:pr_map. pr_eq_repl_back … (λf1:pr_map. f1 ⊆ f2).
27 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
28 [ cases (pr_eq_inv_push_sn … H0 … H1) -g1 /3 width=5 by pr_sle_push/
29 | cases (pr_eq_inv_next_sn … H0 … H1) -g1 /3 width=5 by pr_sle_next/
30 | cases (pr_eq_inv_push_sn … H0 … H1) -g1 /3 width=5 by pr_sle_weak/
34 (*** sle_eq_repl_fwd1 *)
35 lemma pr_sle_eq_repl_fwd_sn:
36 ∀f2. pr_eq_repl_fwd … (λf1. f1 ⊆ f2).
37 #f2 @pr_eq_repl_sym /2 width=3 by pr_sle_eq_repl_back_sn/
40 (*** sle_eq_repl_back2 *)
41 corec lemma pr_sle_eq_repl_back_dx:
42 ∀f1. pr_eq_repl_back … (λf2. f1 ⊆ f2).
44 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
45 [ cases (pr_eq_inv_push_sn … H0 … H2) -g2 /3 width=5 by pr_sle_push/
46 | cases (pr_eq_inv_next_sn … H0 … H2) -g2 /3 width=5 by pr_sle_next/
47 | cases (pr_eq_inv_next_sn … H0 … H2) -g2 /3 width=5 by pr_sle_weak/
51 (*** sle_eq_repl_fwd2 *)
52 lemma pr_sle_eq_repl_fwd_dx:
53 ∀f1. pr_eq_repl_fwd … (λf2. f1 ⊆ f2).
54 #f1 @pr_eq_repl_sym /2 width=3 by pr_sle_eq_repl_back_dx/
59 ∀f1,f2. f1 ≐ f2 → f1 ⊆ f2.
60 /2 width=3 by pr_sle_eq_repl_back_dx/ qed.