src/HOL/ex/cla.ML

--- a/src/HOL/ex/cla.ML	Fri Apr 04 11:18:19 1997 +0200
+++ b/src/HOL/ex/cla.ML	Fri Apr 04 11:18:52 1997 +0200
@@ -13,17 +13,17 @@
 set_current_thy "HOL";  (*Boosts efficiency by omitting redundant rules*)
 
 goal HOL.thy "(P --> Q | R) --> (P-->Q) | (P-->R)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*If and only if*)
 
 goal HOL.thy "(P=Q) = (Q=P::bool)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 goal HOL.thy "~ (P = (~P))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 
@@ -40,112 +40,112 @@
 writeln"Pelletier's examples";
 (*1*)
 goal HOL.thy "(P-->Q)  =  (~Q --> ~P)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*2*)
 goal HOL.thy "(~ ~ P) =  P";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*3*)
 goal HOL.thy "~(P-->Q) --> (Q-->P)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*4*)
 goal HOL.thy "(~P-->Q)  =  (~Q --> P)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*5*)
 goal HOL.thy "((P|Q)-->(P|R)) --> (P|(Q-->R))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*6*)
 goal HOL.thy "P | ~ P";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*7*)
 goal HOL.thy "P | ~ ~ ~ P";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*8.  Peirce's law*)
 goal HOL.thy "((P-->Q) --> P)  -->  P";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*9*)
 goal HOL.thy "((P|Q) & (~P|Q) & (P| ~Q)) --> ~ (~P | ~Q)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*10*)
 goal HOL.thy "(Q-->R) & (R-->P&Q) & (P-->Q|R) --> (P=Q)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*11.  Proved in each direction (incorrectly, says Pelletier!!)  *)
 goal HOL.thy "P=P::bool";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*12.  "Dijkstra's law"*)
 goal HOL.thy "((P = Q) = R) = (P = (Q = R))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*13.  Distributive law*)
 goal HOL.thy "(P | (Q & R)) = ((P | Q) & (P | R))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*14*)
 goal HOL.thy "(P = Q) = ((Q | ~P) & (~Q|P))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*15*)
 goal HOL.thy "(P --> Q) = (~P | Q)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*16*)
 goal HOL.thy "(P-->Q) | (Q-->P)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*17*)
 goal HOL.thy "((P & (Q-->R))-->S)  =  ((~P | Q | S) & (~P | ~R | S))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Classical Logic: examples with quantifiers";
 
 goal HOL.thy "(! x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result(); 
 
 goal HOL.thy "(? x. P-->Q(x))  =  (P --> (? x.Q(x)))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result(); 
 
 goal HOL.thy "(? x.P(x)-->Q) = ((! x.P(x)) --> Q)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result(); 
 
 goal HOL.thy "((! x.P(x)) | Q)  =  (! x. P(x) | Q)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result(); 
 
 (*From Wishnu Prasetya*)
 goal HOL.thy
    "(!s. q(s) --> r(s)) & ~r(s) & (!s. ~r(s) & ~q(s) --> p(t) | q(t)) \
 \   --> p(t) | r(t)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result(); 
 
 
@@ -153,60 +153,60 @@
 
 (*Needs multiple instantiation of the quantifier.*)
 goal HOL.thy "(! x. P(x)-->P(f(x)))  &  P(d)-->P(f(f(f(d))))";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 (*Needs double instantiation of the quantifier*)
 goal HOL.thy "? x. P(x) --> P(a) & P(b)";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 goal HOL.thy "? z. P(z) --> (! x. P(x))";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 goal HOL.thy "? x. (? y. P(y)) --> P(x)";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 writeln"Hard examples with quantifiers";
 
 writeln"Problem 18";
 goal HOL.thy "? y. ! x. P(y)-->P(x)";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result(); 
 
 writeln"Problem 19";
 goal HOL.thy "? x. ! y z. (P(y)-->Q(z)) --> (P(x)-->Q(x))";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 20";
 goal HOL.thy "(! x y. ? z. ! w. (P(x)&Q(y)-->R(z)&S(w)))     \
 \   --> (? x y. P(x) & Q(y)) --> (? z. R(z))";
-by (Fast_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 21";
 goal HOL.thy "(? x. P-->Q(x)) & (? x. Q(x)-->P) --> (? x. P=Q(x))";
-by (Deepen_tac 1 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 22";
 goal HOL.thy "(! x. P = Q(x))  -->  (P = (! x. Q(x)))";
-by (Fast_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 23";
 goal HOL.thy "(! x. P | Q(x))  =  (P | (! x. Q(x)))";
-by (Best_tac 1);  
+by (Blast_tac 1);  
 result();
 
 writeln"Problem 24";
 goal HOL.thy "~(? x. S(x)&Q(x)) & (! x. P(x) --> Q(x)|R(x)) &  \
 \    (~(? x.P(x)) --> (? x.Q(x))) & (! x. Q(x)|R(x) --> S(x))  \
 \   --> (? x. P(x)&R(x))";
-by (Fast_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 25";
@@ -215,14 +215,14 @@
 \       (! x. P(x) --> (M(x) & L(x))) &   \
 \       ((! x. P(x)-->Q(x)) | (? x. P(x)&R(x)))  \
 \   --> (? x. Q(x)&P(x))";
-by (Best_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 26";
 goal HOL.thy "((? x. p(x)) = (? x. q(x))) &     \
 \     (! x. ! y. p(x) & q(y) --> (r(x) = s(y))) \
 \ --> ((! x. p(x)-->r(x)) = (! x. q(x)-->s(x)))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 27";
@@ -231,7 +231,7 @@
 \             (! x. M(x) & L(x) --> P(x)) &   \
 \             ((? x. R(x) & ~ Q(x)) --> (! x. L(x) --> ~ R(x)))  \
 \         --> (! x. M(x) --> ~L(x))";
-by (Fast_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 28.  AMENDED";
@@ -239,21 +239,21 @@
 \       ((! x. Q(x)|R(x)) --> (? x. Q(x)&S(x))) &  \
 \       ((? x.S(x)) --> (! x. L(x) --> M(x)))  \
 \   --> (! x. P(x) & L(x) --> M(x))";
-by (Fast_tac 1);  
+by (Blast_tac 1);  
 result();
 
 writeln"Problem 29.  Essentially the same as Principia Mathematica *11.71";
 goal HOL.thy "(? x. F(x)) & (? y. G(y))  \
 \   --> ( ((! x. F(x)-->H(x)) & (! y. G(y)-->J(y)))  =   \
 \         (! x y. F(x) & G(y) --> H(x) & J(y)))";
-by (Fast_tac 1); 
+by (Blast_tac 1); 
 result();
 
 writeln"Problem 30";
 goal HOL.thy "(! x. P(x) | Q(x) --> ~ R(x)) & \
 \       (! x. (Q(x) --> ~ S(x)) --> P(x) & R(x))  \
 \   --> (! x. S(x))";
-by (Fast_tac 1);  
+by (Blast_tac 1);  
 result();
 
 writeln"Problem 31";
@@ -261,7 +261,7 @@
 \       (? x. L(x) & P(x)) & \
 \       (! x. ~ R(x) --> M(x))  \
 \   --> (? x. L(x) & M(x))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 32";
@@ -269,13 +269,13 @@
 \       (! x. S(x) & R(x) --> L(x)) & \
 \       (! x. M(x) --> R(x))  \
 \   --> (! x. P(x) & M(x) --> L(x))";
-by (Best_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 33";
 goal HOL.thy "(! x. P(a) & (P(x)-->P(b))-->P(c))  =    \
 \    (! x. (~P(a) | P(x) | P(c)) & (~P(a) | ~P(b) | P(c)))";
-by (Best_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 34  AMENDED (TWICE!!)";
@@ -284,13 +284,13 @@
 \                   ((? x. q(x)) = (! y. p(y))))   =    \
 \                  ((? x. ! y. q(x) = q(y))  =          \
 \                   ((? x. p(x)) = (! y. q(y))))";
-by (Deepen_tac 3 1);
+by (Blast_tac 1);
 (*slower with smaller bounds*)
 result();
 
 writeln"Problem 35";
 goal HOL.thy "? x y. P x y -->  (! u v. P u v)";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 36";
@@ -299,7 +299,7 @@
 \       (! x y. J x y | G x y -->       \
 \       (! z. J y z | G y z --> H x z))   \
 \   --> (! x. ? y. H x y)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 37";
@@ -308,7 +308,7 @@
 \       (! x z. ~(P x z) --> (? y. Q y z)) & \
 \       ((? x y. Q x y) --> (! x. R x x))  \
 \   --> (! x. ? y. R x y)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 38";
@@ -318,35 +318,36 @@
 \    (! x. (~p(a) | p(x) | (? z. ? w. p(z) & r x w & r w z)) &  \
 \          (~p(a) | ~(? y. p(y) & r x y) |                      \
 \           (? z. ? w. p(z) & r x w & r w z)))";
-by (Deepen_tac 0 1);  (*beats fast_tac!*)
+by (Blast_tac 1);  (*beats fast_tac!*)
 result();
 
 writeln"Problem 39";
 goal HOL.thy "~ (? x. ! y. F y x = (~ F y y))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 40.  AMENDED";
 goal HOL.thy "(? y. ! x. F x y = F x x)  \
 \       -->  ~ (! x. ? y. ! z. F z y = (~ F z x))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 41";
 goal HOL.thy "(! z. ? y. ! x. f x y = (f x z & ~ f x x))        \
 \              --> ~ (? z. ! x. f x z)";
-by (Best_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 42";
 goal HOL.thy "~ (? y. ! x. p x y = (~ (? z. p x z & p z x)))";
-by (Deepen_tac 3 1);
+by (Blast_tac 1);
 result();
 
-writeln"Problem 43  NOT PROVED AUTOMATICALLY";
+writeln"Problem 43!!";
 goal HOL.thy
     "(! x::'a. ! y::'a. q x y = (! z. p z x = (p z y::bool)))   \
 \ --> (! x. (! y. q x y = (q y x::bool)))";
+by (Blast_tac 1);
 
 
 writeln"Problem 44";
@@ -354,7 +355,7 @@
 \             (? y. g(y) & h x y & (? y. g(y) & ~ h x y)))  &   \
 \             (? x. j(x) & (! y. g(y) --> h x y))               \
 \             --> (? x. j(x) & ~f(x))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 45";
@@ -365,7 +366,7 @@
 \    (? x. f(x) & (! y. h x y --> l(y))                         \
 \               & (! y. g(y) & h x y --> j x y))                \
 \     --> (? x. f(x) & ~ (? y. g(y) & h x y))";
-by (Best_tac 1); 
+by (Blast_tac 1); 
 result();
 
 
@@ -373,7 +374,7 @@
 
 writeln"Problem 48";
 goal HOL.thy "(a=b | c=d) & (a=c | b=d) --> a=d | b=c";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 49  NOT PROVED AUTOMATICALLY";
@@ -386,20 +387,20 @@
 by (assume_tac 1);
 by (res_inst_tac [("x","b")] allE 1);
 by (assume_tac 1);
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 50";  
 (*What has this to do with equality?*)
 goal HOL.thy "(! x. P a x | (! y.P x y)) --> (? x. ! y.P x y)";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 51";
 goal HOL.thy
     "(? z w. ! x y. P x y = (x=z & y=w)) -->  \
 \    (? z. ! x. ? w. (! y. P x y = (y=w)) = (x=z))";
-by (Best_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 52";
@@ -407,7 +408,7 @@
 goal HOL.thy
     "(? z w. ! x y. P x y = (x=z & y=w)) -->  \
 \    (? w. ! y. ? z. (! x. P x y = (x=z)) = (y=w))";
-by (Best_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 55";
@@ -423,20 +424,20 @@
 \  (!x. hates agatha x --> hates butler x) & \
 \  (!x. ~hates x agatha | ~hates x butler | ~hates x charles) --> \
 \   killed ?who agatha";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 56";
 goal HOL.thy
     "(! x. (? y. P(y) & x=f(y)) --> P(x)) = (! x. P(x) --> P(f(x)))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 57";
 goal HOL.thy
     "P (f a b) (f b c) & P (f b c) (f a c) & \
 \    (! x y z. P x y & P y z --> P x z)    -->   P (f a b) (f a c)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 58  NOT PROVED AUTOMATICALLY";
@@ -447,13 +448,13 @@
 
 writeln"Problem 59";
 goal HOL.thy "(! x. P(x) = (~P(f(x)))) --> (? x. P(x) & ~P(f(x)))";
-by (Deepen_tac 1 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 60";
 goal HOL.thy
     "! x. P x (f x) = (? y. (! z. P z y --> P z (f x)) & P x y)";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 writeln"Problem 62 as corrected in JAR 18 (1997), page 135";
@@ -461,7 +462,7 @@
     "(ALL x. p a & (p x --> p(f x)) --> p(f(f x)))  =   \
 \    (ALL x. (~ p a | p x | p(f(f x))) &                        \
 \            (~ p a | ~ p(f x) | p(f(f x))))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 (*From Rudnicki, Obvious Inferences, JAR 3 (1987), 383-393.  
@@ -470,14 +471,14 @@
     "(ALL x. F(x) & ~G(x) --> (EX y. H(x,y) & J(y))) &        \
 \    (EX x. K(x) & F(x) & (ALL y. H(x,y) --> K(y)))  &        \
 \    (ALL x. K(x) --> ~G(x))   -->   (EX x. K(x) --> ~G(x))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();
 
 goal Prod.thy
     "(ALL x y. R(x,y) | R(y,x)) &                \
 \    (ALL x y. S(x,y) & S(y,x) --> x=y) &        \
 \    (ALL x y. R(x,y) --> S(x,y))    -->   (ALL x y. S(x,y) --> R(x,y))";
-by (Fast_tac 1);
+by (Blast_tac 1);
 result();