src/HOL/ex/Puzzle.ML
changeset 1820 e381e1c51689
parent 1673 d22110ddd0af
child 2017 dd3e2a91aeca
equal deleted inserted replaced
1819:245721624c8d 1820:e381e1c51689
    19 by (Simp_tac 1);
    19 by (Simp_tac 1);
    20 by (rtac impI 1);
    20 by (rtac impI 1);
    21 by (rtac classical 1);
    21 by (rtac classical 1);
    22 by (dtac not_leE 1);
    22 by (dtac not_leE 1);
    23 by (subgoal_tac "f(na) <= f(f(na))" 1);
    23 by (subgoal_tac "f(na) <= f(f(na))" 1);
    24 by (best_tac (HOL_cs addIs [lessD,Puzzle.f_ax,le_less_trans,le_trans]) 1);
    24 by (best_tac (!claset addIs [lessD,Puzzle.f_ax,le_less_trans,le_trans]) 1);
    25 by (fast_tac (HOL_cs addIs [Puzzle.f_ax]) 1);
    25 by (fast_tac (!claset addIs [Puzzle.f_ax]) 1);
    26 val lemma = result() RS spec RS mp;
    26 val lemma = result() RS spec RS mp;
    27 
    27 
    28 goal Puzzle.thy "n <= f(n)";
    28 goal Puzzle.thy "n <= f(n)";
    29 by (fast_tac (HOL_cs addIs [lemma]) 1);
    29 by (fast_tac (!claset addIs [lemma]) 1);
    30 qed "lemma1";
    30 qed "lemma1";
    31 
    31 
    32 goal Puzzle.thy "f(n) < f(Suc(n))";
    32 goal Puzzle.thy "f(n) < f(Suc(n))";
    33 by (fast_tac (HOL_cs addIs [Puzzle.f_ax,le_less_trans,lemma1]) 1);
    33 by (fast_tac (!claset addIs [Puzzle.f_ax,le_less_trans,lemma1]) 1);
    34 qed "lemma2";
    34 qed "lemma2";
    35 
    35 
    36 val prems = goal Puzzle.thy "(!!n.f(n) <= f(Suc(n))) ==> m<n --> f(m) <= f(n)";
    36 val prems = goal Puzzle.thy "(!!n.f(n) <= f(Suc(n))) ==> m<n --> f(m) <= f(n)";
    37 by (res_inst_tac[("n","n")]nat_induct 1);
    37 by (res_inst_tac[("n","n")]nat_induct 1);
    38 by (Simp_tac 1);
    38 by (Simp_tac 1);
    39 by (simp_tac (!simpset addsimps [less_Suc_eq]) 1);
    39 by (simp_tac (!simpset addsimps [less_Suc_eq]) 1);
    40 by (fast_tac (HOL_cs addIs (le_trans::prems)) 1);
    40 by (fast_tac (!claset addIs (le_trans::prems)) 1);
    41 bind_thm("mono_lemma1", result() RS mp);
    41 bind_thm("mono_lemma1", result() RS mp);
    42 
    42 
    43 val [p1,p2] = goal Puzzle.thy
    43 val [p1,p2] = goal Puzzle.thy
    44     "[| !! n. f(n)<=f(Suc(n));  m<=n |] ==> f(m) <= f(n)";
    44     "[| !! n. f(n)<=f(Suc(n));  m<=n |] ==> f(m) <= f(n)";
    45 by (rtac (p2 RS le_imp_less_or_eq RS disjE) 1);
    45 by (rtac (p2 RS le_imp_less_or_eq RS disjE) 1);
    46 by (etac (p1 RS mono_lemma1) 1);
    46 by (etac (p1 RS mono_lemma1) 1);
    47 by (fast_tac (HOL_cs addIs [le_refl]) 1);
    47 by (fast_tac (!claset addIs [le_refl]) 1);
    48 qed "mono_lemma";
    48 qed "mono_lemma";
    49 
    49 
    50 val prems = goal Puzzle.thy "m <= n ==> f(m) <= f(n)";
    50 val prems = goal Puzzle.thy "m <= n ==> f(m) <= f(n)";
    51 by (fast_tac (HOL_cs addIs ([mono_lemma,less_imp_le,lemma2]@prems)) 1);
    51 by (fast_tac (!claset addIs ([mono_lemma,less_imp_le,lemma2]@prems)) 1);
    52 qed "f_mono";
    52 qed "f_mono";
    53 
    53 
    54 goal Puzzle.thy "f(n) = n";
    54 goal Puzzle.thy "f(n) = n";
    55 by (rtac le_anti_sym 1);
    55 by (rtac le_anti_sym 1);
    56 by (rtac lemma1 2);
    56 by (rtac lemma1 2);
    57 by (fast_tac (HOL_cs addIs [Puzzle.f_ax,leI] addDs [leD,f_mono,lessD]) 1);
    57 by (fast_tac (!claset addIs [Puzzle.f_ax,leI] addDs [leD,f_mono,lessD]) 1);
    58 result();
    58 result();