elim (lpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
elim (tdeq_dec h o T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
[ elim (tdeq_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
- /4 width=7 by fsb_fpbs_trans, tdeq_lfdeq_lpx_fpbs, fpbs_fqup_trans/
+ /4 width=7 by fsb_fpbs_trans, tdeq_rdeq_lpx_fpbs, fpbs_fqup_trans/
| elim (cpxs_tdneq_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
/3 width=14 by fpbs_cpxs_tdeq_fqup_lpx_trans/
(* Advanced eliminators *****************************************************)
-lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
+lemma csx_ind_fpb: ∀h,o. ∀Q:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
+ (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T.
+ ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → Q G L T.
/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
-lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
+lemma csx_ind_fpbg: ∀h,o. ∀Q:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
+ (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T.
+ ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → Q G L T.
/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.