(* Main destructions with ifr ***********************************************)
-theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐢𝐟[⊗p,⊗q] ▼[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #k * #H1k #Ht1 #Ht2
-@(ex_intro … (↑♭q)) @and3_intro
-[ -H0t1 -Ht1 -Ht2
+theorem dfr_des_ifr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+ t1 ➡𝐝𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H0t1
+* #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (↑♭q))
+[ -H0t1 -H1k -Ht1 -Ht2 //
+| -H0t1 -Ht1 -Ht2
>structure_L_sn
>H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #Ht1 //
| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
@(subset_eq_trans … Ht2) -t2
- @(subset_eq_trans … (unwind2_term_fsubst …))
+ @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
[ @fsubst_eq_repl [ // | // ]
@(subset_eq_trans … (unwind2_term_iref …))
@(subset_eq_canc_sn … (lift_term_eq_repl_dx …))