include "ground/relocation/gr_isi_id.ma".
include "ground/relocation/gr_pat_pat_id.ma".
-(* IDENTITY CONDITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+(* IDENTITY CONDITION FOR GENERIC RELOCATION MAPS ***************************)
-(* Advanced properties on isid **********************************************)
+(* Advanced constructions with gr_isi ***************************************)
(*** isid_at *)
lemma gr_isi_pat (f): (∀i. @❪i,f❫ ≘ i) → 𝐈❪f❫.
/3 width=1 by gr_eq_id_isi, gr_pat_inv_id/
qed.
-(* Inversion lemmas on pat ****************************************)
+(* Inversions with gr_pat ***************************************************)
(*** isid_inv_at *)
lemma gr_isi_inv_pat (f) (i): 𝐈❪f❫ → @❪i,f❫ ≘ i.
/3 width=3 by gr_isi_inv_eq_id, gr_pat_id, gr_pat_eq_repl_back/
qed-.
-(* Destructions with pat *)
+(* Destructions with gr_pat *************************************************)
(*** isid_inv_at_mono *)
lemma gr_isi_pat_des (f) (i1) (i2): 𝐈❪f❫ → @❪i1,f❫ ≘ i2 → i1 = i2.