author  wenzelm 
Wed, 05 May 1999 18:48:32 +0200  
changeset 6604  d646567156c3 
parent 6121  5fe77b9b5185 
permissions  rwrr 
6121
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

1 
(**** FOL examples ****) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

2 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

3 
Pretty.setmargin 72; (*existing macros just allow this margin*) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

4 
print_depth 0; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

5 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

6 
(*** Intuitionistic examples ***) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

7 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

8 
context IFOL.thy; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

9 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

10 
(*Quantifier example from Logic&Computation*) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

11 
Goal "(EX y. ALL x. Q(x,y)) > (ALL x. EX y. Q(x,y))"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

12 
by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

13 
by (resolve_tac [allI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

14 
by (resolve_tac [exI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

15 
by (eresolve_tac [exE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

16 
choplev 2; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

17 
by (eresolve_tac [exE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

18 
by (resolve_tac [exI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

19 
by (eresolve_tac [allE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

20 
by (assume_tac 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

21 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

22 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

23 
(*Example of Dyckhoff's method*) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

24 
Goalw [not_def] "~ ~ ((P>Q)  (Q>P))"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

25 
by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

26 
by (eresolve_tac [disj_impE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

27 
by (eresolve_tac [imp_impE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

28 
by (eresolve_tac [imp_impE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

29 
by (REPEAT (eresolve_tac [FalseE] 2)); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

30 
by (assume_tac 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

31 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

32 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

33 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

34 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

35 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

36 
(*** Classical examples ***) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

37 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

38 
context FOL.thy; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

39 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

40 
Goal "EX y. ALL x. P(y)>P(x)"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

41 
by (resolve_tac [exCI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

42 
by (resolve_tac [allI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

43 
by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

44 
by (eresolve_tac [allE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

45 
prth (allI RSN (2,swap)); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

46 
by (eresolve_tac [it] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

47 
by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

48 
by (eresolve_tac [notE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

49 
by (assume_tac 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

50 
Goal "EX y. ALL x. P(y)>P(x)"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

51 
by (Blast_tac 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

52 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

53 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

54 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

55 
 Goal "EX y. ALL x. P(y)>P(x)"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

56 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

57 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

58 
1. EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

59 
 by (resolve_tac [exCI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

60 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

61 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

62 
1. ALL y. ~(ALL x. P(y) > P(x)) ==> ALL x. P(?a) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

63 
 by (resolve_tac [allI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

64 
Level 2 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

65 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

66 
1. !!x. ALL y. ~(ALL x. P(y) > P(x)) ==> P(?a) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

67 
 by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

68 
Level 3 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

69 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

70 
1. !!x. [ ALL y. ~(ALL x. P(y) > P(x)); P(?a) ] ==> P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

71 
 by (eresolve_tac [allE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

72 
Level 4 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

73 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

74 
1. !!x. [ P(?a); ~(ALL xa. P(?y3(x)) > P(xa)) ] ==> P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

75 
 prth (allI RSN (2,swap)); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

76 
[ ~(ALL x. ?P1(x)); !!x. ~?Q ==> ?P1(x) ] ==> ?Q 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

77 
 by (eresolve_tac [it] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

78 
Level 5 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

79 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

80 
1. !!x xa. [ P(?a); ~P(x) ] ==> P(?y3(x)) > P(xa) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

81 
 by (resolve_tac [impI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

82 
Level 6 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

83 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

84 
1. !!x xa. [ P(?a); ~P(x); P(?y3(x)) ] ==> P(xa) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

85 
 by (eresolve_tac [notE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

86 
Level 7 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

87 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

88 
1. !!x xa. [ P(?a); P(?y3(x)) ] ==> P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

89 
 by (assume_tac 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

90 
Level 8 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

91 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

92 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

93 
 Goal "EX y. ALL x. P(y)>P(x)"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

94 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

95 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

96 
1. EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

97 
 by (best_tac FOL_dup_cs 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

98 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

99 
EX y. ALL x. P(y) > P(x) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

100 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

101 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

102 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

103 
(**** finally, the example FOL/ex/if.ML ****) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

104 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

105 
> val prems = goalw if_thy [if_def] 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

106 
# "[ P ==> Q; ~P ==> R ] ==> if(P,Q,R)"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

107 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

108 
if(P,Q,R) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

109 
1. P & Q  ~P & R 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

110 
> by (Classical.fast_tac (FOL_cs addIs prems) 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

111 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

112 
if(P,Q,R) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

113 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

114 
> val ifI = result(); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

115 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

116 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

117 
> val major::prems = goalw if_thy [if_def] 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

118 
# "[ if(P,Q,R); [ P; Q ] ==> S; [ ~P; R ] ==> S ] ==> S"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

119 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

120 
S 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

121 
1. S 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

122 
> by (cut_facts_tac [major] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

123 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

124 
S 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

125 
1. P & Q  ~P & R ==> S 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

126 
> by (Classical.fast_tac (FOL_cs addIs prems) 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

127 
Level 2 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

128 
S 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

129 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

130 
> val ifE = result(); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

131 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

132 
> goal if_thy "if(P, if(Q,A,B), if(Q,C,D)) <> if(Q, if(P,A,C), if(P,B,D))"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

133 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

134 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

135 
1. if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

136 
> by (resolve_tac [iffI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

137 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

138 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

139 
1. if(P,if(Q,A,B),if(Q,C,D)) ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

140 
2. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

141 
> by (eresolve_tac [ifE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

142 
Level 2 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

143 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

144 
1. [ P; if(Q,A,B) ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

145 
2. [ ~P; if(Q,C,D) ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

146 
3. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

147 
> by (eresolve_tac [ifE] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

148 
Level 3 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

149 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

150 
1. [ P; Q; A ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

151 
2. [ P; ~Q; B ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

152 
3. [ ~P; if(Q,C,D) ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

153 
4. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

154 
> by (resolve_tac [ifI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

155 
Level 4 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

156 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

157 
1. [ P; Q; A; Q ] ==> if(P,A,C) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

158 
2. [ P; Q; A; ~Q ] ==> if(P,B,D) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

159 
3. [ P; ~Q; B ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

160 
4. [ ~P; if(Q,C,D) ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

161 
5. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

162 
> by (resolve_tac [ifI] 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

163 
Level 5 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

164 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

165 
1. [ P; Q; A; Q; P ] ==> A 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

166 
2. [ P; Q; A; Q; ~P ] ==> C 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

167 
3. [ P; Q; A; ~Q ] ==> if(P,B,D) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

168 
4. [ P; ~Q; B ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

169 
5. [ ~P; if(Q,C,D) ] ==> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

170 
6. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

171 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

172 
> choplev 0; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

173 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

174 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

175 
1. if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

176 
> val if_cs = FOL_cs addSIs [ifI] addSEs[ifE]; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

177 
> by (Classical.fast_tac if_cs 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

178 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

179 
if(P,if(Q,A,B),if(Q,C,D)) <> if(Q,if(P,A,C),if(P,B,D)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

180 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

181 
> val if_commute = result(); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

182 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

183 
> goal if_thy "if(if(P,Q,R), A, B) <> if(P, if(Q,A,B), if(R,A,B))"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

184 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

185 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

186 
1. if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

187 
> by (Classical.fast_tac if_cs 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

188 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

189 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

190 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

191 
> val nested_ifs = result(); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

192 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

193 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

194 
> choplev 0; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

195 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

196 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

197 
1. if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

198 
> by (rewrite_goals_tac [if_def]); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

199 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

200 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

201 
1. (P & Q  ~P & R) & A  ~(P & Q  ~P & R) & B <> 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

202 
P & (Q & A  ~Q & B)  ~P & (R & A  ~R & B) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

203 
> by (Classical.fast_tac FOL_cs 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

204 
Level 2 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

205 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,A,B)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

206 
No subgoals! 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

207 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

208 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

209 
> goal if_thy "if(if(P,Q,R), A, B) <> if(P, if(Q,A,B), if(R,B,A))"; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

210 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

211 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

212 
1. if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

213 
> by (REPEAT (Classical.step_tac if_cs 1)); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

214 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

215 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

216 
1. [ A; ~P; R; ~P; R ] ==> B 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

217 
2. [ B; ~P; ~R; ~P; ~R ] ==> A 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

218 
3. [ ~P; R; B; ~P; R ] ==> A 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

219 
4. [ ~P; ~R; A; ~B; ~P ] ==> R 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

220 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

221 
> choplev 0; 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

222 
Level 0 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

223 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

224 
1. if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

225 
> by (rewrite_goals_tac [if_def]); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

226 
Level 1 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

227 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

228 
1. (P & Q  ~P & R) & A  ~(P & Q  ~P & R) & B <> 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

229 
P & (Q & A  ~Q & B)  ~P & (R & B  ~R & A) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

230 
> by (Classical.fast_tac FOL_cs 1); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

231 
by: tactic failed 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

232 
Exception ERROR raised 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

233 
Exception failure raised 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

234 

5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

235 
> by (REPEAT (Classical.step_tac FOL_cs 1)); 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

236 
Level 2 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

237 
if(if(P,Q,R),A,B) <> if(P,if(Q,A,B),if(R,B,A)) 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

238 
1. [ A; ~P; R; ~P; R; ~False ] ==> B 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

239 
2. [ A; ~P; R; R; ~False; ~B; ~B ] ==> Q 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

240 
3. [ B; ~P; ~R; ~P; ~A ] ==> R 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

241 
4. [ B; ~P; ~R; ~Q; ~A ] ==> R 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

242 
5. [ B; ~R; ~P; ~A; ~R; Q; ~False ] ==> A 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

243 
6. [ ~P; R; B; ~P; R; ~False ] ==> A 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

244 
7. [ ~P; ~R; A; ~B; ~R ] ==> P 
5fe77b9b5185
the separate FOL and ZF logics manual, with new material on datatypes and
paulson
parents:
diff
changeset

245 
8. [ ~P; ~R; A; ~B; ~R ] ==> Q 