--- a/src/HOL/Nat.thy Wed Feb 05 16:34:56 2025 +0000
+++ b/src/HOL/Nat.thy Thu Feb 06 16:20:52 2025 +0000
@@ -1268,7 +1268,7 @@
lemma diff_is_0_eq' [simp]: "m \<le> n \<Longrightarrow> m - n = 0"
for m n :: nat
- by (rule iffD2, rule diff_is_0_eq)
+ by simp
lemma zero_less_diff [simp]: "0 < n - m \<longleftrightarrow> m < n"
for m n :: nat
@@ -1755,6 +1755,9 @@
by simp
qed
+lemma of_nat_diff_if: \<open>of_nat (m - n) = (if n\<le>m then of_nat m - of_nat n else 0)\<close>
+ by (simp add: not_le less_imp_le)
+
end
text \<open>Class for unital semirings with characteristic zero.