#n <nplus_comm // qed.
lemma nplus_succ_shift (m) (n): โm + n = m + โn.
-// qed-.
+// qed.
(*** assoc_plus1 *)
lemma nplus_plus_comm_12 (o) (m) (n): m + n + o = n + (m + o).
(*** plus_plus_comm_23 *)
lemma nplus_plus_comm_23 (o) (m) (n): o + m + n = o + n + m.
#o #m #n >nplus_assoc >nplus_assoc <nplus_comm in โข (??(??%)?); //
-qed-.
+qed.
(* Basic inversions *********************************************************)
-(*** plus_inv_O3 zero_eq_plus *)
+(*** zero_eq_plus *)
lemma eq_inv_zero_nplus (m) (n): ๐ = m + n โ โงโง ๐ = m & ๐ = n.
#m #n @(nat_ind_succ โฆ n) -n
[ /2 width=1 by conj/
]
qed-.
+(*** plus_inv_O3 *)
+lemma eq_inv_nplus_zero (m) (n):
+ m + n = ๐ โ โงโง ๐ = m & ๐ = n.
+/2 width=1 by eq_inv_zero_nplus/ qed-.
+
(*** injective_plus_l *)
lemma eq_inv_nplus_bi_dx (o) (m) (n): m + o = n + o โ m = n.
#o @(nat_ind_succ โฆ o) -o /3 width=1 by eq_inv_nsucc_bi/