--- a/src/HOL/Nat.thy Sun Mar 22 19:31:13 2020 +0000
+++ b/src/HOL/Nat.thy Mon Mar 23 10:25:56 2020 +0000
@@ -2458,6 +2458,7 @@
lemma nat_mult_1_right: "n * 1 = n"
for n :: nat
by (fact mult_1_right)
+
lemma diff_mult_distrib: "(m - n) * k = (m * k) - (n * k)"
for k m n :: nat
by (fact left_diff_distrib')
@@ -2466,6 +2467,11 @@
for k m n :: nat
by (fact right_diff_distrib')
+(*Used in AUTO2 and Groups.le_diff_conv2 (with variables renamed) doesn't work for some reason*)
+lemma le_diff_conv2: "k \<le> j \<Longrightarrow> (i \<le> j - k) = (i + k \<le> j)"
+ for i j k :: nat
+ by (fact le_diff_conv2)
+
lemma diff_self_eq_0 [simp]: "m - m = 0"
for m :: nat
by (fact diff_cancel)