include "ground/relocation/gr_tls.ma".
include "ground/relocation/gr_pat.ma".
-(**) (* it should not depend on gr_isi *)
+(* * it should not depend on gr_isi *)
include "ground/relocation/gr_isi_uni.ma".
include "ground/relocation/gr_after_isi.ma".
-(* RELATIONAL COMPOSITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+(* RELATIONAL COMPOSITION FOR GENERIC RELOCATION MAPS ***********************)
-(* Properties with pat and uni and tls *******************************************************)
+(* Constructions with gr_pat and gr_uni and gr_tls **************************)
(*** after_uni_succ_dx *)
lemma gr_after_pat_uni (i2) (i1):
∀f2. @❪i1, f2❫ ≘ i2 →
- â\88\80f. f2 â\8a\9a ð\9d\90®â\9d¨i1â\9d© â\89\98 f â\86\92 ð\9d\90®â\9d¨i2â\9d© â\8a\9a ⫱*[i2] f2 ≘ f.
+ â\88\80f. f2 â\8a\9a ð\9d\90®â\9d¨i1â\9d© â\89\98 f â\86\92 ð\9d\90®â\9d¨i2â\9d© â\8a\9a â«°*[i2] f2 ≘ f.
#i2 elim i2 -i2
[ #i1 #f2 #Hf2 #f #Hf
elim (gr_pat_inv_unit_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct
(*** after_uni_succ_sn *)
lemma gr_pat_after_uni_tls (i2) (i1):
∀f2. @❪i1, f2❫ ≘ i2 →
- â\88\80f. ð\9d\90®â\9d¨i2â\9d© â\8a\9a ⫱*[i2] f2 ≘ f → f2 ⊚ 𝐮❨i1❩ ≘ f.
+ â\88\80f. ð\9d\90®â\9d¨i2â\9d© â\8a\9a â«°*[i2] f2 ≘ f → f2 ⊚ 𝐮❨i1❩ ≘ f.
#i2 elim i2 -i2
[ #i1 #f2 #Hf2 #f #Hf
elim (gr_pat_inv_unit_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct
]
qed-.
-(* Advanced properties with uni *)
+(* Advanced constructions with gr_uni ***************************************)
(*** after_uni_one_dx *)
lemma gr_after_push_unit: