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_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_constructors.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 ************************************************)
-theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
- t1 Ļµ š ā t1ā(pāš¦) Ļµ š ā
- t1 ā”š[p,q] t2 ā ā¼[f]t1 ā”š[āp,āq] ā¼[f]t2.
-#f #p #q #t1 #t2 #H1t1 #H2t1
+lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
+ t1 Ļµ š ā t1ā(pāš¦) Ļµ š ā
+ t1 ā”š¢š[p,q] t2 ā ā¼[f]t1 ā”š¢š[āp,āq] ā¼[f]t2.
+#f #p #q #t1 #t2 #H1t1 #H2t1
* #n * #H1n #Ht1 #Ht2
-@(ex_intro ā¦ (āāāq)) @and3_intro
-[ -H0t1 -Ht1 -Ht2
+@(ex_intro ā¦ (āāq)) @and3_intro
+[ -H1t1 -H2t1 -Ht1 -Ht2
>structure_L_sn >structure_reverse
>H1n >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H0t1
- <unwind2_path_d_dx <depth_structure
+| lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1t1 -H2t1
+ <unwind2_path_d_dx
>list_append_rcons_sn in H1n; <reverse_append #H1n
lapply (unwind2_rmap_append_pap_closed f ā¦ H1n)
<reverse_lcons <depth_L_dx #H2n
@(subset_eq_trans ā¦ Ht2) -t2
@(subset_eq_trans ā¦ (unwind2_term_fsubst ā¦))
[ @fsubst_eq_repl [ // | // ]
-(*
- @(subset_eq_trans ā¦ (unwind2_term_iref ā¦))
@(subset_eq_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
[ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
- @(subset_eq_trans ā¦ (unwind2_lift_term_after ā¦))
+ @(subset_eq_trans ā¦ (lift_unwind2_term_after ā¦))
+ @(subset_eq_canc_dx ā¦ (unwind2_term_after_lift ā¦))
@unwind2_term_eq_repl_sn
(* Note: crux of the proof begins *)
@nstream_eq_inv_ext #m
>list_append_rcons_sn in H1n; <reverse_append #H1n
lapply (unwind2_rmap_append_pap_closed f ā¦ H1n) #H2n
>nrplus_inj_dx in ā¢ (???%); <H2n -H2n
- lapply (tls_unwind2_rmap_append_closed f ā¦ H1n) #H2n
- <(tr_pap_eq_repl ā¦ H2n) -H2n -H1n //
+ lapply (tls_unwind2_rmap_append_closed f ā¦ H1n) -H1n #H2n
+ <(tr_pap_eq_repl ā¦ H2n) -H2n //
(* Note: crux of the proof ends *)
-*)
| //
| /2 width=2 by ex_intro/
- | //
+ | /2 width=6 by lift_term_proper/
]
]
qed.