include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/unwind/unwind2_constructors.ma".
include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_inner.ma".
+include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
include "delayed_updating/unwind/unwind2_rmap_head.ma".
include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_proper.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
-include "delayed_updating/syntax/prototerm_proper_inner.ma".
include "delayed_updating/syntax/path_head_structure.ma".
include "delayed_updating/syntax/path_structure_depth.ma".
include "delayed_updating/syntax/path_structure_reverse.ma".
(* Constructions with unwind ************************************************)
lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
- t1 ϵ 𝐓 → t1⋔(p◖𝗦) ⧸≬ 𝐈 →
- t1 â\9e¡ð\9d\90\9f[p,q] t2 â\86\92 â\96¼[f]t1 â\9e¡𝐟[⊗p,⊗q] ▼[f]t2.
+ t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
+ t1 â\9e¡ð\9d\90¢ð\9d\90\9f[p,q] t2 â\86\92 â\96¼[f]t1 â\9e¡ð\9d\90¢𝐟[⊗p,⊗q] ▼[f]t2.
#f #p #q #t1 #t2 #H1t1 #H2t1
* #n * #H1n #Ht1 #Ht2
@(ex_intro … (↑♭q)) @and3_intro
@(subset_eq_trans … Ht2) -t2
@(subset_eq_trans … (unwind2_term_fsubst …))
[ @fsubst_eq_repl [ // | // ]
- @(subset_eq_canc_dx … (unwind2_term_after …))
- @(subset_eq_canc_sn … (unwind2_term_eq_repl_dx …))
+ @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
[ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
- @(subset_eq_trans … (unwind2_term_after …))
+ @(subset_eq_trans … (lift_unwind2_term_after …))
+ @(subset_eq_canc_dx … (unwind2_term_after_lift …))
@unwind2_term_eq_repl_sn
(* Note: crux of the proof begins *)
@nstream_eq_inv_ext #m
(* Note: crux of the proof ends *)
| //
| /2 width=2 by ex_intro/
- | @term_proper_outer #H0 (**) (* full auto does not work *)
- /3 width=2 by unwind2_term_des_inner/
+ | /2 width=6 by lift_term_proper/
]
]
qed.