src/FOL/ex/nat.ML

-(*  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();