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basic_2: stronger supclosure allows better inversion lemmas
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14
15 include "basic_2/grammar/lenv_length.ma".
16 include "basic_2/s_transition/fqu.ma".
17
18 (* SUPCLOSURE ***************************************************************)
19
20 (* Forward lemmas with length for local environments ************************)
21
22 fact fqu_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
23                                ∀i. T1 = #i → |L2| < |L1|.
24 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 // [2: #p]
25 #I #G #L #V #T #j #H destruct
26 qed-.
27
28 lemma fqu_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐ ⦃G2, L2, T2⦄ →
29                             |L2| < |L1|.
30 /2 width=7 by fqu_fwd_length_lref1_aux/
31 qed-.
32
33 (* Inversion lemmas with length for local environments **********************)
34
35 fact fqu_inv_eq_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
36                      G1 = G2 → |L1| = |L2| → T1 = T2 → ⊥.
37 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
38 [1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
39 |5: #I #G #L #V #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
40 ]
41 /2 width=4 by discr_tpair_xy_y, discr_tpair_xy_x/
42 qed-.
43
44 lemma fqu_inv_eq: ∀G,L1,L2,T. ⦃G, L1, T⦄ ⊐ ⦃G, L2, T⦄ → |L1| = |L2| → ⊥.
45 #G #L1 #L2 #T #H #H0 @(fqu_inv_eq_aux … H … H0) // (**) (* full auto fails *)
46 qed-.