src/HOL/ex/Mutil.ML

 
 goal thy "!!t. t: tiling A ==> \
 \              u: tiling A --> t <= Compl u --> t Un u : tiling A";
 by (etac tiling.induct 1);
 by (Simp_tac 1);
-by (fast_tac (!claset addIs tiling.intrs
-                      addss (!simpset addsimps [Un_assoc])) 1);
+by (simp_tac (!simpset addsimps [Un_assoc]) 1);
+by (blast_tac (!claset addIs tiling.intrs) 1);
 qed_spec_mp "tiling_UnI";
 
 
 (*** Chess boards ***)
 

 Addsimps [below_0, below_Suc];
 
 goal thy "ALL i. (i: below k) = (i<k)";
 by (nat_ind_tac "k" 1);
 by (ALLGOALS (asm_simp_tac (!simpset addsimps [less_Suc_eq])));
-by (Fast_tac 1);
+by (Blast_tac 1);
 qed_spec_mp "below_less_iff";
 
 Addsimps [below_less_iff];
 
 goal thy "below(Suc n) Times B = ({n} Times B) Un ((below n) Times B)";
 by (Simp_tac 1);
-by (Fast_tac 1);
+by (Blast_tac 1);
 qed "Sigma_Suc1";
 
 goal thy "A Times below(Suc n) = (A Times {n}) Un (A Times (below n))";
 by (Simp_tac 1);
-by (Fast_tac 1);
+by (Blast_tac 1);
 qed "Sigma_Suc2";
 
 (*Deletion is essential to allow use of Sigma_Suc1,2*)
 Delsimps [below_Suc];
 

 by (resolve_tac tiling.intrs 1);
 by (assume_tac 2);
 by (subgoal_tac    (*seems the easiest way of turning one to the other*)
     "({i} Times {Suc(n1+n1)}) Un ({i} Times {n1+n1}) = \
 \    {(i, n1+n1), (i, Suc(n1+n1))}" 1);
-by (Fast_tac 2);
+by (Blast_tac 2);
 by (asm_simp_tac (!simpset addsimps [domino.horiz]) 1);
-by (fast_tac (!claset addEs  [less_asym]
-                      addSDs [below_less_iff RS iffD1]) 1);
+by (blast_tac (!claset addEs  [less_irrefl, less_asym]
+                       addSDs [below_less_iff RS iffD1]) 1);
 qed "dominoes_tile_row";
 
 goal thy "(below m) Times below(n + n) : tiling domino";
 by (nat_ind_tac "m" 1);
 by (ALLGOALS (asm_simp_tac (!simpset addsimps [Sigma_Suc1])));
-by (fast_tac (!claset addIs [equalityI, tiling_UnI, dominoes_tile_row] 
-                      addEs [below_less_iff RS iffD1 RS less_irrefl]) 1);
+by (blast_tac (!claset addSIs [tiling_UnI, dominoes_tile_row]
+                      addSEs [below_less_iff RS iffD1 RS less_irrefl]) 1);
 qed "dominoes_tile_matrix";
 
 
 (*** Basic properties of evnodd ***)
 

 
 (* finite X ==> finite(evnodd X b) *)
 bind_thm("finite_evnodd", evnodd_subset RS finite_subset);
 
 goalw thy [evnodd_def] "evnodd (A Un B) b = evnodd A b Un evnodd B b";
-by (Fast_tac 1);
+by (Blast_tac 1);
 qed "evnodd_Un";
 
 goalw thy [evnodd_def] "evnodd (A - B) b = evnodd A b - evnodd B b";
-by (Fast_tac 1);
+by (Blast_tac 1);
 qed "evnodd_Diff";
 
 goalw thy [evnodd_def] "evnodd {} b = {}";
 by (Simp_tac 1);
 qed "evnodd_empty";

 by (REPEAT_FIRST assume_tac);
 (*Four similar cases: case (i+j) mod 2 = b, 2#-b, ...*)
 by (REPEAT (asm_full_simp_tac (!simpset addsimps
                           [less_Suc_eq, evnodd_insert, evnodd_empty, mod_Suc] 
                           setloop split_tac [expand_if]) 1
-           THEN Fast_tac 1));
+           THEN Blast_tac 1));
 qed "domino_singleton";
 
 goal thy "!!d. d:domino ==> finite d";
-by (fast_tac (!claset addSIs [finite_insertI, finite_emptyI] 
-                      addEs [domino.elim]) 1);
+by (blast_tac (!claset addSIs [finite_insertI, finite_emptyI] 
+                      addSEs [domino.elim]) 1);
 qed "domino_finite";
 
 
 (*** Tilings of dominoes ***)
 
 goal thy "!!t. t:tiling domino ==> finite t";
 by (eresolve_tac [tiling.induct] 1);
 by (rtac finite_emptyI 1);
-by (fast_tac (!claset addIs [domino_finite, finite_UnI]) 1);
+by (blast_tac (!claset addSIs [finite_UnI] addIs [domino_finite]) 1);
 qed "tiling_domino_finite";
 
 goal thy "!!t. t: tiling domino ==> card(evnodd t 0) = card(evnodd t 1)";
 by (eresolve_tac [tiling.induct] 1);
 by (simp_tac (!simpset addsimps [evnodd_def]) 1);

 by (subgoal_tac "ALL p b. p : evnodd a b --> p ~: evnodd ta b" 1);
 by (asm_simp_tac (!simpset addsimps [evnodd_Un, Un_insert_left, 
                                      tiling_domino_finite,
                                      evnodd_subset RS finite_subset,
                                      card_insert_disjoint]) 1);
-by (fast_tac (!claset addSDs [evnodd_subset RS subsetD] addEs [equalityE]) 1);
+by (blast_tac (!claset addSDs [evnodd_subset RS subsetD] addEs [equalityE]) 1);
 qed "tiling_domino_0_1";
 
 goal thy "!!m n. [| t = below(Suc m + Suc m) Times below(Suc n + Suc n);   \
 \                   t' = t - {(0,0)} - {(Suc(m+m), Suc(n+n))}              \
 \                |] ==> t' ~: tiling domino";