diff -r 3904cfde1aa9 -r f3fe59e61f3d src/HOL/Nat.thy --- 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 \ j \ (i \ j - k) = (i + k \ 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)