src/FOL/ex/Nat.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Nat.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,69 @@
+(*  Title: 	FOL/ex/nat.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Examples for the manual "Introduction to Isabelle"
+
+Proofs about the natural numbers
+
+INCOMPATIBLE with nat2.ML, Nipkow's examples
+
+To generate similar output to manual, execute these commands:
+    Pretty.setmargin 72; print_depth 0;
+*)
+
+open Nat;
+
+goal Nat.thy "~ (Suc(k) = k)";
+by (res_inst_tac [("n","k")] induct 1);
+by (resolve_tac [notI] 1);
+by (eresolve_tac [Suc_neq_0] 1);
+by (resolve_tac [notI] 1);
+by (eresolve_tac [notE] 1);
+by (eresolve_tac [Suc_inject] 1);
+val Suc_n_not_n = result();
+
+
+goal Nat.thy "(k+m)+n = k+(m+n)";
+prths ([induct] RL [topthm()]);  (*prints all 14 next states!*)
+by (resolve_tac [induct] 1);
+back();
+back();
+back();
+back();
+back();
+back();
+
+goalw Nat.thy [add_def] "0+n = n";
+by (resolve_tac [rec_0] 1);
+val add_0 = result();
+
+goalw Nat.thy [add_def] "Suc(m)+n = Suc(m+n)";
+by (resolve_tac [rec_Suc] 1);
+val add_Suc = result();
+
+val add_ss = FOL_ss  addsimps  [add_0, add_Suc];
+
+goal Nat.thy "(k+m)+n = k+(m+n)";
+by (res_inst_tac [("n","k")] induct 1);
+by (simp_tac add_ss 1);
+by (asm_simp_tac add_ss 1);
+val add_assoc = result();
+
+goal Nat.thy "m+0 = m";
+by (res_inst_tac [("n","m")] induct 1);
+by (simp_tac add_ss 1);
+by (asm_simp_tac add_ss 1);
+val add_0_right = result();
+
+goal Nat.thy "m+Suc(n) = Suc(m+n)";
+by (res_inst_tac [("n","m")] induct 1);
+by (ALLGOALS (asm_simp_tac add_ss));
+val add_Suc_right = result();
+
+val [prem] = goal Nat.thy "(!!n. f(Suc(n)) = Suc(f(n))) ==> f(i+j) = i+f(j)";
+by (res_inst_tac [("n","i")] induct 1);
+by (simp_tac add_ss 1);
+by (asm_simp_tac (add_ss addsimps [prem]) 1);
+result();