put back Nat.le_diff_conv2 because AUTO2 doesn't work with Groups.le_diff_conv2
authorpaulson <lp15@cam.ac.uk>
Mon, 23 Mar 2020 10:25:56 +0000
changeset 71588 f3fe59e61f3d
parent 71587 3904cfde1aa9
child 71589 5d1370b32975
put back Nat.le_diff_conv2 because AUTO2 doesn't work with Groups.le_diff_conv2
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 \<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)