src/HOL/Fun.ML

 
 (*** inj(f): f is a one-to-one function ***)
 
 val prems = goalw Fun.thy [inj_def]
     "[| !! x y. f(x) = f(y) ==> x=y |] ==> inj(f)";
-by (fast_tac (!claset addIs prems) 1);
+by (blast_tac (!claset addIs prems) 1);
 qed "injI";
 
 val [major] = goal Fun.thy "(!!x. g(f(x)) = x) ==> inj(f)";
 by (rtac injI 1);
 by (etac (arg_cong RS box_equals) 1);

 
 (*** inj_onto f A: f is one-to-one over A ***)
 
 val prems = goalw Fun.thy [inj_onto_def]
     "(!! x y. [| f(x) = f(y);  x:A;  y:A |] ==> x=y) ==> inj_onto f A";
-by (fast_tac (!claset addIs prems) 1);
+by (blast_tac (!claset addIs prems) 1);
 qed "inj_ontoI";
 
 val [major] = goal Fun.thy 
     "(!!x. x:A ==> g(f(x)) = x) ==> inj_onto f A";
 by (rtac inj_ontoI 1);

 by (rtac (major RS bspec RS bspec RS mp) 1);
 by (REPEAT (resolve_tac prems 1));
 qed "inj_ontoD";
 
 goal Fun.thy "!!x y.[| inj_onto f A;  x:A;  y:A |] ==> (f(x)=f(y)) = (x=y)";
-by (fast_tac (!claset addSEs [inj_ontoD]) 1);
+by (blast_tac (!claset addSDs [inj_ontoD]) 1);
 qed "inj_onto_iff";
 
 val major::prems = goal Fun.thy
     "[| inj_onto f A;  ~x=y;  x:A;  y:A |] ==> ~ f(x)=f(y)";
 by (rtac contrapos 1);

     "!!f g. [| inj(f);  inj_onto g (range f) |] ==> inj(g o f)";
 by (fast_tac (!claset addIs [injI] addEs [injD, inj_ontoD]) 1);
 qed "comp_inj";
 
 val [prem] = goal Fun.thy "inj(f) ==> inj_onto f A";
-by (fast_tac (!claset addIs [prem RS injD, inj_ontoI]) 1);
+by (blast_tac (!claset addIs [prem RS injD, inj_ontoI]) 1);
 qed "inj_imp";
 
 val [prem] = goalw Fun.thy [inv_def] "y : range(f) ==> f(inv f y) = y";
 by (EVERY1 [rtac (prem RS rangeE), rtac selectI, etac sym]);
 qed "f_inv_f";

     "[| inv f x=inv f y; x: range(f);  y: range(f) |] ==> x=y";
 by (rtac (arg_cong RS box_equals) 1);
 by (REPEAT (resolve_tac (prems @ [f_inv_f]) 1));
 qed "inv_injective";
 
-val prems = goal Fun.thy
-    "[| inj(f);  A<=range(f) |] ==> inj_onto (inv f) A";
-by (cut_facts_tac prems 1);
+goal Fun.thy "!!f. [| inj(f);  A<=range(f) |] ==> inj_onto (inv f) A";
 by (fast_tac (!claset addIs [inj_ontoI] 
                       addEs [inv_injective,injD]) 1);
 qed "inj_onto_inv";