(*** at_basic_lt *)
lemma pr_pat_basic_lt (m) (n) (i):
- ninj i ≤ m → @❨i, 𝐛❨m,n❩❩ ≘ i.
+ ninj i ≤ m → @⧣❨i, 𝐛❨m,n❩❩ ≘ 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 → @❨i, 𝐛❨m,n❩❩ ≘ i+n.
+ m < ninj i → @⧣❨i, 𝐛❨m,n❩❩ ≘ 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 ≤ m → @❨i, 𝐛❨m,n❩❩ ≘ j → i = j.
+ ninj i ≤ m → @⧣❨i, 𝐛❨m,n❩❩ ≘ 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 → @❨i, 𝐛❨m,n❩❩ ≘ j → i+n = j.
+ m < ninj i → @⧣❨i, 𝐛❨m,n❩❩ ≘ j → i+n = j.
/3 width=4 by pr_pat_basic_ge, pr_pat_mono/ qed-.