1 include "basic_2/computation/fpbc.ma".
3 (* Advanced eliminators *****************************************************)
5 fact csx_ind_fpbc_aux: ∀h,g. ∀R:relation3 genv lenv term.
6 (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
7 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
10 ∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
11 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G2 L2 T2.
12 #h #g #R #IH1 #G1 #L1 #T1 #H @(csx_ind … H) -T1
13 #T1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
14 #G1 #L1 #T1 #IH2 #H1 #IH3 #G2 #L2 #T2 #H12 @IH1 -IH1 /2 width=5 by csx_fqus_conf/
16 [ #G0 #L0 #T0 #H20 lapply (fqus_fqup_trans … H12 H20) -G2 -L2 -T2
17 #H10 @(IH2 … H10) -IH2 /2 width=5 by csx_fqup_conf/
18 #T2 #HT02 #H #G3 #L3 #T3 #HT23 elim (fqup_cpx_trans_neq … H10 … HT02 H) -T0
19 /4 width=8 by fqup_fqus_trans, fqup_fqus/
20 | #T0 #HT20 #H elim (fqus_cpxs_trans_neq … H12 … HT20 H) -T2 /3 width=4 by/
24 lemma csx_ind_fpbc: ∀h,g. ∀R:relation3 genv lenv term.
25 (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
26 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
29 ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
30 /4 width=8 by csx_ind_fpbc_fqus/ qed-.