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/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/syntax/path_head_structure.ma".
include "delayed_updating/syntax/path_structure_depth.ma".
include "delayed_updating/syntax/path_structure_reverse.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".
-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
>list_append_rcons_sn in H1n; <reverse_append #H1n
lapply (unwind2_rmap_append_pap_closed f ā¦ H1n)
<reverse_lcons <depth_L_dx #H2n
>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¦ Ht2) -t2
@(subset_eq_trans ā¦ (unwind2_term_fsubst ā¦))
[ @fsubst_eq_repl [ // | // ]
@(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_canc_sn ā¦ (lift_term_eq_repl_dx ā¦))
[ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
- 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 //
+ @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
+ @tr_compose_eq_repl
+ [ <unwind2_rmap_append_pap_closed //
+ | >unwind2_rmap_A_sn <reverse_rcons
+ /2 width=1 by tls_unwind2_rmap_append_closed/
+ ]