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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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15 include "basic_2/relocation/fquq_alt.ma".
16 include "basic_2/substitution/fqus.ma".
18 (* STAR-ITERATED SUPCLOSURE *************************************************)
20 (* Advanced inversion lemmas ************************************************)
22 lemma fqus_inv_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
23 ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
24 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
25 #G #G2 #L #L2 #T #T2 #_ #H2 * elim (fquq_inv_gen … H2) -H2
26 [ /3 width=5 by fqup_strap1, or_introl/
27 | * #HG #HL #HT destruct /2 width=1 by or_introl/
28 | #H2 * #HG #HL #HT destruct /3 width=1 by fqu_fqup, or_introl/
29 | * #H1G #H1L #H1T * #H2G #H2L #H2T destruct /2 width=1 by or_intror/
33 (* Advanced properties ******************************************************)
35 lemma fqus_strap1_fqu: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐ ⦃G2, L2, T2⦄ →
36 ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
37 #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_gen … H1) -H1
38 [ /2 width=5 by fqup_strap1/
39 | * #HG #HL #HT destruct /2 width=1 by fqu_fqup/
43 lemma fqus_strap2_fqu: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ →
44 ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
45 #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_gen … H2) -H2
46 [ /2 width=5 by fqup_strap2/
47 | * #HG #HL #HT destruct /2 width=1 by fqu_fqup/
51 lemma fqus_fqup_trans: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+ ⦃G2, L2, T2⦄ →
52 ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
53 #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fqup_ind … H2) -H2 -G2 -L2 -T2
54 /2 width=5 by fqus_strap1_fqu, fqup_strap1/
57 lemma fqup_fqus_trans: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G, L, T⦄ →
58 ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
59 #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 @(fqup_ind_dx … H1) -H1 -G1 -L1 -T1
60 /3 width=5 by fqus_strap2_fqu, fqup_strap2/