doc-src/TutorialI/IsarOverview/Isar/Calc.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/IsarOverview/Isar/Calc.thy	Mon Sep 09 17:28:29 2002 +0200
@@ -0,0 +1,30 @@
+theory Calc = Main:
+
+axclass
+  group < zero, plus, minus
+  assoc:       "(x + y) + z = x + (y + z)"
+  left_0:      "0 + x = x"
+  left_minus:  "-x + x = 0"
+
+theorem right_minus: "x + -x = (0::'a::group)"
+proof -
+  have   "x + -x = (-(-x) + -x) + (x + -x)"
+    by (simp only: left_0 left_minus)
+  also have "... = -(-x) + ((-x + x) + -x)"
+    by (simp only: group.assoc)
+  also have "... = 0"
+    by (simp only: left_0 left_minus)
+  finally show ?thesis .
+qed
+
+
+lemma assumes R: "(a,b) \<in> R" "(b,c) \<in> R" "(c,d) \<in> R"
+      shows "(a,d) \<in> R\<^sup>*"
+proof -
+       have "(a,b) \<in> R\<^sup>*" ..
+  also have "(b,c) \<in> R\<^sup>*" ..
+  also have "(c,d) \<in> R\<^sup>*" ..
+  finally show ?thesis .
+qed
+
+end
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