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15 include "basic_2/relocation/fsup.ma".
17 (* PLUS-ITERATED SUPCLOSURE *************************************************)
19 definition fsupp: bi_relation lenv term ≝ bi_TC … fsup.
21 interpretation "plus-iterated structural successor (closure)"
22 'SupTermPlus L1 T1 L2 T2 = (fsupp L1 T1 L2 T2).
24 (* Basic eliminators ********************************************************)
26 lemma fsupp_ind: ∀L1,T1. ∀R:relation2 lenv term.
27 (∀L2,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → R L2 T2) →
28 (∀L,T,L2,T2. ⦃L1, T1⦄ ⊃+ ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ → R L T → R L2 T2) →
29 ∀L2,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → R L2 T2.
30 #L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
31 @(bi_TC_ind … IH1 IH2 ? ? H)
34 lemma fsupp_ind_dx: ∀L2,T2. ∀R:relation2 lenv term.
35 (∀L1,T1. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → R L1 T1) →
36 (∀L1,L,T1,T. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃+ ⦃L2, T2⦄ → R L T → R L1 T1) →
37 ∀L1,T1. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → R L1 T1.
38 #L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
39 @(bi_TC_ind_dx … IH1 IH2 ? ? H)
42 (* Basic properties *********************************************************)
44 lemma fsup_fsupp: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
47 lemma fsupp_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃+ ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ →
51 lemma fsupp_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃+ ⦃L2, T2⦄ →
55 (* Basic forward lemmas *****************************************************)
57 lemma fsupp_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → ♯{L2, T2} < ♯{L1, T1}.
58 #L1 #L2 #T1 #T2 #H @(fsupp_ind … H) -L2 -T2
59 /3 width=3 by fsup_fwd_cw, transitive_lt/