(*** at_basic_lt *)
lemma pr_pat_basic_lt (m) (n) (i):
- ninj i â\89¤ m â\86\92 @â\9dªi, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d« ≘ i.
+ ninj i â\89¤ m â\86\92 @â\9d¨i, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d© ≘ i.
#m #n #i >(npsucc_pred i) #Hmi
/2 width=1 by pr_nat_basic_lt/
qed.
(*** at_basic_ge *)
lemma pr_pat_basic_ge (m) (n) (i):
- m < ninj i â\86\92 @â\9dªi, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d« ≘ i+n.
+ m < ninj i â\86\92 @â\9d¨i, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d© ≘ i+n.
#m #n #i >(npsucc_pred i) #Hmi <nrplus_npsucc_sn
/3 width=1 by pr_nat_basic_ge, nlt_inv_succ_dx/
qed.
(*** at_basic_inv_lt *)
lemma pr_pat_basic_inv_lt (m) (n) (i) (j):
- ninj i â\89¤ m â\86\92 @â\9dªi, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d« ≘ j → i = j.
+ ninj i â\89¤ m â\86\92 @â\9d¨i, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d© ≘ j → i = j.
/3 width=4 by pr_pat_basic_lt, pr_pat_mono/ qed-.
(*** at_basic_inv_ge *)
lemma pr_pat_basic_inv_ge (m) (n) (i) (j):
- m < ninj i â\86\92 @â\9dªi, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d« ≘ j → i+n = j.
+ m < ninj i â\86\92 @â\9d¨i, ð\9d\90\9bâ\9d¨m,nâ\9d©â\9d© ≘ j → i+n = j.
/3 width=4 by pr_pat_basic_ge, pr_pat_mono/ qed-.