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14
15 include "ground/relocation/pr_sle_sle.ma".
16 include "ground/relocation/pr_sor.ma".
17
18 (* RELATIONAL UNION FOR PARTIAL RELOCATION MAPS *****************************)
19
20 (* Inversions with pr_sle ***************************************************)
21
22 (*** sor_inv_sle_sn *)
23 corec lemma pr_sor_inv_sle_sn:
24             ∀f1,f2,f. f1 ⋓ f2 ≘ f → f1 ⊆ f.
25 #f1 #f2 #f * -f1 -f2 -f
26 #f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0
27 /3 width=5 by pr_sle_push, pr_sle_next, pr_sle_weak/
28 qed-.
29
30 (*** sor_inv_sle_dx *)
31 corec lemma pr_sor_inv_sle_dx:
32             ∀f1,f2,f. f1 ⋓ f2 ≘ f → f2 ⊆ f.
33 #f1 #f2 #f * -f1 -f2 -f
34 #f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0
35 /3 width=5 by pr_sle_push, pr_sle_next, pr_sle_weak/
36 qed-.
37
38 (*** sor_inv_sle_sn_trans *)
39 lemma pr_sor_inv_sle_sn_trans:
40       ∀f1,f2,f. f1 ⋓ f2 ≘ f → ∀g. g ⊆ f1 → g ⊆ f.
41 /3 width=4 by pr_sor_inv_sle_sn, pr_sle_trans/ qed-.
42
43 (*** sor_inv_sle_dx_trans *)
44 lemma pr_sor_inv_sle_dx_trans:
45       ∀f1,f2,f. f1 ⋓ f2 ≘ f → ∀g. g ⊆ f2 → g ⊆ f.
46 /3 width=4 by pr_sor_inv_sle_dx, pr_sle_trans/ qed-.
47
48 (*** sor_inv_sle *)
49 axiom pr_sor_inv_sle_bi:
50       ∀f1,f2,f. f1 ⋓ f2 ≘ f → ∀g. f1 ⊆ g → f2 ⊆ g → f ⊆ g.
51
52 (* Constructions with pr_sle ************************************************)
53
54 (*** sor_sle_dx *)
55 corec lemma pr_sor_sle_dx:
56             ∀f1,f2. f1 ⊆ f2 → f1 ⋓ f2 ≘ f2.
57 #f1 #f2 * -f1 -f2
58 /3 width=7 by pr_sor_push_bi, pr_sor_next_bi, pr_sor_push_next/
59 qed.
60
61 (*** sor_sle_sn *)
62 corec lemma pr_sor_sle_sn:
63             ∀f1,f2. f1 ⊆ f2 → f2 ⋓ f1 ≘ f2.
64 #f1 #f2 * -f1 -f2
65 /3 width=7 by pr_sor_push_bi, pr_sor_next_bi, pr_sor_next_push/
66 qed.