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15 notation "hvbox( ⦃ L1, break T1 ⦄ > + break ⦃ L2 , break T2 ⦄ )"
16 non associative with precedence 45
17 for @{ 'SupTermPlus $L1 $T1 $L2 $T2 }.
19 include "basic_2/substitution/csup.ma".
21 (* PLUS-ITERATED SUPCLOSURE *************************************************)
23 definition csupp: bi_relation lenv term ≝ bi_TC … csup.
25 interpretation "plus-iterated structural predecessor (closure)"
26 'SupTermPlus L1 T1 L2 T2 = (csupp L1 T1 L2 T2).
28 (* Basic eliminators ********************************************************)
30 lemma csupp_ind: ∀L1,T1. ∀R:relation2 lenv term.
31 (∀L2,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → R L2 T2) →
32 (∀L,T,L2,T2. ⦃L1, T1⦄ >+ ⦃L, T⦄ → ⦃L, T⦄ > ⦃L2, T2⦄ → R L T → R L2 T2) →
33 ∀L2,T2. ⦃L1, T1⦄ >+ ⦃L2, T2⦄ → R L2 T2.
34 #L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
35 @(bi_TC_ind … IH1 IH2 ? ? H)
38 lemma csupp_ind_dx: ∀L2,T2. ∀R:relation2 lenv term.
39 (∀L1,T1. ⦃L1, T1⦄ > ⦃L2, T2⦄ → R L1 T1) →
40 (∀L1,L,T1,T. ⦃L1, T1⦄ > ⦃L, T⦄ → ⦃L, T⦄ >+ ⦃L2, T2⦄ → R L T → R L1 T1) →
41 ∀L1,T1. ⦃L1, T1⦄ >+ ⦃L2, T2⦄ → R L1 T1.
42 #L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
43 @(bi_TC_ind_dx … IH1 IH2 ? ? H)
46 (* Basic properties *********************************************************)
48 lemma csup_csupp: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ⦃L1, T1⦄ >+ ⦃L2, T2⦄.
51 lemma csupp_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ >+ ⦃L, T⦄ → ⦃L, T⦄ > ⦃L2, T2⦄ →
55 lemma csupp_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ > ⦃L, T⦄ → ⦃L, T⦄ >+ ⦃L2, T2⦄ →
59 (* Basic forward lemmas *****************************************************)
61 lemma csupp_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ >+ ⦃L2, T2⦄ → #{L2, T2} < #{L1, T1}.
62 #L1 #L2 #T1 #T2 #H @(csupp_ind … H) -L2 -T2
63 /3 width=3 by csup_fwd_cw, transitive_lt/