(* RELOCATION MAP ***********************************************************)
-definition basic: nat â\86\92 nat â\86\92 rtmap â\89\9d λm,n. ⫯*[m] ð\9d\90\94â\9d´nâ\9dµ.
+definition basic: nat â\86\92 nat â\86\92 rtmap â\89\9d λm,n. ⫯*[m] ð\9d\90\94â\9d¨nâ\9d©.
interpretation "basic relocation (rtmap)"
'Basic m n = (basic m n).
(* Prioerties with application **********************************************)
-lemma at_basic_lt: â\88\80m,n,i. i < m â\86\92 @â¦\83i, ð\9d\90\81â\9d´m,nâ\9dµâ¦\84 ≘ i.
+lemma at_basic_lt: â\88\80m,n,i. i < m â\86\92 @â\9dªi, ð\9d\90\81â\9d¨m,nâ\9d©â\9d« ≘ i.
#m elim m -m [ #n #i #H elim (lt_zero_false … H) ]
#m #IH #n * [ /2 width=2 by refl, at_refl/ ]
#i #H lapply (lt_S_S_to_lt … H) -H /3 width=7 by refl, at_push/
qed.
-lemma at_basic_ge: â\88\80m,n,i. m â\89¤ i â\86\92 @â¦\83i, ð\9d\90\81â\9d´m,nâ\9dµâ¦\84 ≘ n+i.
+lemma at_basic_ge: â\88\80m,n,i. m â\89¤ i â\86\92 @â\9dªi, ð\9d\90\81â\9d¨m,nâ\9d©â\9d« ≘ n+i.
#m elim m -m //
#m #IH #n #j #H
elim (le_inv_S1 … H) -H #i #Hmi #H destruct
(* Inversion lemmas with application ****************************************)
-lemma at_basic_inv_lt: â\88\80m,n,i,j. i < m â\86\92 @â¦\83i, ð\9d\90\81â\9d´m,nâ\9dµâ¦\84 ≘ j → i = j.
+lemma at_basic_inv_lt: â\88\80m,n,i,j. i < m â\86\92 @â\9dªi, ð\9d\90\81â\9d¨m,nâ\9d©â\9d« ≘ j → i = j.
/3 width=4 by at_basic_lt, at_mono/ qed-.
-lemma at_basic_inv_ge: â\88\80m,n,i,j. m â\89¤ i â\86\92 @â¦\83i, ð\9d\90\81â\9d´m,nâ\9dµâ¦\84 ≘ j → n+i = j.
+lemma at_basic_inv_ge: â\88\80m,n,i,j. m â\89¤ i â\86\92 @â\9dªi, ð\9d\90\81â\9d¨m,nâ\9d©â\9d« ≘ j → n+i = j.
/3 width=4 by at_basic_ge, at_mono/ qed-.