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1 (* Advanced inversion lemmas on plus-iterated supclosure ********************)
2
3 lamma fsupp_inv_bind1_fsups: ∀b,J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓑ{b,J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
4                              ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ ⊃* ⦃G2, L2, T2⦄.
5 #b #J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
6 [ #G2 #L2 #T2 #H
7   elim (fsup_inv_bind1 … H) -H * #H1 #H2 #H3 destruct /2 width=1/
8 | #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
9 ]
10 qad-.
11
12 lamma fsupp_inv_flat1_fsups: ∀J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓕ{J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
13                              ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, U⦄ ⊃* ⦃G2, L2, T2⦄.
14 #J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
15 [ #G2 #L2 #T2 #H
16   elim (fsup_inv_flat1 … H) -H #H1 * #H2 destruct /2 width=1/
17 | #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
18 ]
19 qad-.
20
21 lamma fsupp_fsups: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
22 /2 width=1 by tri_inj/ qed.
23
24 lamma fsups_lref: ∀I,G,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊃* ⦃G, K, V⦄.
25 /3 width=5 by _/ qed.
26
27 lamma fsups_lref_S_lt: ∀I,G1,G2,L,K,V,T,i.
28                        0 < i → ⦃G1, L, #(i-1)⦄ ⊃* ⦃G2, K, T⦄ → ⦃G1, L.ⓑ{I}V, #i⦄ ⊃+ ⦃G2, K, T⦄.
29 /3 width=7 by _/ qed.