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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/substitution/ldrop_ldrop.ma".
16 include "basic_2/substitution/csup.ma".
18 (* SUPCLOSURE ***************************************************************)
20 (* Advanced inversion lemmas ************************************************)
22 lemma csup_inv_ldrop: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
23 ∀J,W,j. ⇩[0, j] L1 ≡ L2.ⓑ{J}W → T1 = #j ∧ T2 = W.
24 #L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
25 [ #I #L #K #V #i #HLKV #J #W #j #HLKW
26 elim (ldrop_conf_div … HLKV … HLKW) -L /2 width=1/
30 #I #L #V #T #J #W #j #H
31 lapply (ldrop_pair2_fwd_cw … H W) -H #H
32 [2: lapply (transitive_lt (#{L,W}) … H) /2 width=1/ -H #H ]
33 elim (lt_refl_false … H)
36 (* Main forward lemmas ******************************************************)
38 theorem csup_trans_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
39 ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ →
40 L = L0 ∨ ⦃L, T1⦄ > ⦃L, T3⦄.
41 #L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
42 [ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
43 lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
44 lapply (csup_fwd_cw … H) -H #H2
45 lapply (transitive_lt … H1 H2) -H1 -H2 #H
46 elim (lt_refl_false … H)
47 | #a #I #L0 #V2 #T2 #T3 #HT23
48 elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/