doc-src/AxClass/Nat/NatClass.ML
author wenzelm
Tue Sep 19 23:15:28 2006 +0200 (2006-09-19)
changeset 20622 e1a573146be5
parent 10140 ba9297b71897
child 24584 01e83ffa6c54
permissions -rw-r--r--
tuned proofs;
     1 (*  Title:      FOL/ex/NatClass.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 This is Nat.ML with some trivial modifications in order to make it
     6 work with NatClass.thy.
     7 *)
     8 
     9 val induct = thm "induct";
    10 val Suc_inject = thm "Suc_inject";
    11 val Suc_neq_0 = thm "Suc_neq_0";
    12 val rec_0 = thm "rec_0";
    13 val rec_Suc = thm "rec_Suc";
    14 val add_def = thm "add_def";
    15 
    16 
    17 Goal "Suc(k) ~= (k::'a::nat)";
    18 by (res_inst_tac [("n","k")] induct 1);
    19 by (rtac notI 1);
    20 by (etac Suc_neq_0 1);
    21 by (rtac notI 1);
    22 by (etac notE 1);
    23 by (etac Suc_inject 1);
    24 qed "Suc_n_not_n";
    25 
    26 
    27 Goal "(k+m)+n = k+(m+n)";
    28 prths ([induct] RL [topthm()]);  (*prints all 14 next states!*)
    29 by (rtac induct 1);
    30 back();
    31 back();
    32 back();
    33 back();
    34 back();
    35 back();
    36 
    37 Goalw [add_def] "\\<zero>+n = n";
    38 by (rtac rec_0 1);
    39 qed "add_0";
    40 
    41 Goalw [add_def] "Suc(m)+n = Suc(m+n)";
    42 by (rtac rec_Suc 1);
    43 qed "add_Suc";
    44 
    45 Addsimps [add_0, add_Suc];
    46 
    47 Goal "(k+m)+n = k+(m+n)";
    48 by (res_inst_tac [("n","k")] induct 1);
    49 by (Simp_tac 1);
    50 by (Asm_simp_tac 1);
    51 qed "add_assoc";
    52 
    53 Goal "m+\\<zero> = m";
    54 by (res_inst_tac [("n","m")] induct 1);
    55 by (Simp_tac 1);
    56 by (Asm_simp_tac 1);
    57 qed "add_0_right";
    58 
    59 Goal "m+Suc(n) = Suc(m+n)";
    60 by (res_inst_tac [("n","m")] induct 1);
    61 by (ALLGOALS (Asm_simp_tac));
    62 qed "add_Suc_right";
    63 
    64 val [prem] = Goal "(!!n. f(Suc(n)) = Suc(f(n))) ==> f(i+j) = i+f(j)";
    65 by (res_inst_tac [("n","i")] induct 1);
    66 by (Simp_tac 1);
    67 by (asm_simp_tac (simpset() addsimps [prem]) 1);
    68 qed "";
    69