author  wenzelm 
Sun, 01 Mar 2009 23:36:12 +0100  
changeset 30190  479806475f3c 
parent 28814  463c9e9111ae 
child 30850  5e20f9c20086 
permissions  rwrr 
13404  1 
(* Title: HOL/Tools/rewrite_hol_proof.ML 
2 
ID: $Id$ 

3 
Author: Stefan Berghofer, TU Muenchen 

4 

5 
Rewrite rules for HOL proofs 

6 
*) 

7 

8 
signature REWRITE_HOL_PROOF = 

9 
sig 

10 
val rews: (Proofterm.proof * Proofterm.proof) list 

11 
val elim_cong: typ list > Proofterm.proof > Proofterm.proof option 

12 
end; 

13 

14 
structure RewriteHOLProof : REWRITE_HOL_PROOF = 

15 
struct 

16 

17 
open Proofterm; 

18 

28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

19 
val rews = map (pairself (ProofSyntax.proof_of_term (the_context ()) true) o 
28262
aa7ca36d67fd
back to dynamic the_context(), because static @{theory} is invalidated if ML environment changes within the same code block;
wenzelm
parents:
27253
diff
changeset

20 
Logic.dest_equals o Logic.varify o ProofSyntax.read_term (the_context ()) propT) 
13404  21 

22 
(** eliminate metaequality rules **) 

23 

24 
["(equal_elim % x1 % x2 %% \ 

25 
\ (combination % TYPE('T1) % TYPE('T2) % Trueprop % x3 % A % B %% \ 

28712
4f2954d995f0
Removed argument prf2 in rewrite rules for equal_elim to make them applicable
berghofe
parents:
28262
diff
changeset

26 
\ (axm.reflexive % TYPE('T3) % x4) %% prf1)) == \ 
13404  27 
\ (iffD1 % A % B %% \ 
28712
4f2954d995f0
Removed argument prf2 in rewrite rules for equal_elim to make them applicable
berghofe
parents:
28262
diff
changeset

28 
\ (meta_eq_to_obj_eq % TYPE(bool) % A % B %% prf1))", 
13404  29 

30 
"(equal_elim % x1 % x2 %% (axm.symmetric % TYPE('T1) % x3 % x4 %% \ 

31 
\ (combination % TYPE('T2) % TYPE('T3) % Trueprop % x5 % A % B %% \ 

28712
4f2954d995f0
Removed argument prf2 in rewrite rules for equal_elim to make them applicable
berghofe
parents:
28262
diff
changeset

32 
\ (axm.reflexive % TYPE('T4) % x6) %% prf1))) == \ 
13404  33 
\ (iffD2 % A % B %% \ 
28712
4f2954d995f0
Removed argument prf2 in rewrite rules for equal_elim to make them applicable
berghofe
parents:
28262
diff
changeset

34 
\ (meta_eq_to_obj_eq % TYPE(bool) % A % B %% prf1))", 
13404  35 

36 
"(meta_eq_to_obj_eq % TYPE('U) % x1 % x2 %% \ 

37 
\ (combination % TYPE('U) % TYPE('T) % f % g % x % y %% prf1 %% prf2)) == \ 

38 
\ (cong % TYPE('U) % TYPE('T) % f % g % x % y %% \ 

39 
\ (meta_eq_to_obj_eq % TYPE('T => 'U) % f % g %% prf1) %% \ 

40 
\ (meta_eq_to_obj_eq % TYPE('T) % x % y %% prf2))", 

41 

42 
"(meta_eq_to_obj_eq % TYPE('T) % x1 % x2 %% \ 

43 
\ (axm.transitive % TYPE('T) % x % y % z %% prf1 %% prf2)) == \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

44 
\ (HOL.trans % TYPE('T) % x % y % z %% \ 
13404  45 
\ (meta_eq_to_obj_eq % TYPE('T) % x % y %% prf1) %% \ 
46 
\ (meta_eq_to_obj_eq % TYPE('T) % y % z %% prf2))", 

47 

48 
"(meta_eq_to_obj_eq % TYPE('T) % x % x %% (axm.reflexive % TYPE('T) % x)) == \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

49 
\ (HOL.refl % TYPE('T) % x)", 
13404  50 

51 
"(meta_eq_to_obj_eq % TYPE('T) % x % y %% \ 

52 
\ (axm.symmetric % TYPE('T) % x % y %% prf)) == \ 

53 
\ (sym % TYPE('T) % x % y %% (meta_eq_to_obj_eq % TYPE('T) % x % y %% prf))", 

54 

55 
"(meta_eq_to_obj_eq % TYPE('T => 'U) % x1 % x2 %% \ 

56 
\ (abstract_rule % TYPE('U) % TYPE('T) % f % g %% prf)) == \ 

57 
\ (ext % TYPE('U) % TYPE('T) % f % g %% \ 

58 
\ (Lam (x::'T). meta_eq_to_obj_eq % TYPE('U) % f x % g x %% (prf % x)))", 

59 

60 
"(meta_eq_to_obj_eq % TYPE('T) % x % y %% \ 

61 
\ (eq_reflection % TYPE('T) % x % y %% prf)) == prf", 

62 

63 
"(meta_eq_to_obj_eq % TYPE('T1) % x1 % x2 %% (equal_elim % x3 % x4 %% \ 

64 
\ (combination % TYPE(prop) % TYPE('T) % x7 % x8 % C % D %% \ 

65 
\ (combination % TYPE('T3) % TYPE('T) % op == % op == % A % B %% \ 

66 
\ (axm.reflexive % TYPE('T4) % op ==) %% prf1) %% prf2) %% prf3)) == \ 

67 
\ (iffD1 % A = C % B = D %% \ 

68 
\ (cong % TYPE(bool) % TYPE('T::type) % op = A % op = B % C % D %% \ 

69 
\ (cong % TYPE('T=>bool) % TYPE('T) % \ 

70 
\ (op = :: 'T=>'T=>bool) % (op = :: 'T=>'T=>bool) % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

71 
\ (HOL.refl % TYPE('T=>'T=>bool) % (op = :: 'T=>'T=>bool)) %% \ 
13404  72 
\ (meta_eq_to_obj_eq % TYPE('T) % A % B %% prf1)) %% \ 
73 
\ (meta_eq_to_obj_eq % TYPE('T) % C % D %% prf2)) %% \ 

74 
\ (meta_eq_to_obj_eq % TYPE('T) % C % D %% prf3))", 

75 

76 
"(meta_eq_to_obj_eq % TYPE('T1) % x1 % x2 %% (equal_elim % x3 % x4 %% \ 

77 
\ (axm.symmetric % TYPE('T2) % x5 % x6 %% \ 

78 
\ (combination % TYPE(prop) % TYPE('T) % x7 % x8 % C % D %% \ 

79 
\ (combination % TYPE('T3) % TYPE('T) % op == % op == % A % B %% \ 

80 
\ (axm.reflexive % TYPE('T4) % op ==) %% prf1) %% prf2)) %% prf3)) == \ 

81 
\ (iffD2 % A = C % B = D %% \ 

82 
\ (cong % TYPE(bool) % TYPE('T::type) % op = A % op = B % C % D %% \ 

83 
\ (cong % TYPE('T=>bool) % TYPE('T) % \ 

84 
\ (op = :: 'T=>'T=>bool) % (op = :: 'T=>'T=>bool) % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

85 
\ (HOL.refl % TYPE('T=>'T=>bool) % (op = :: 'T=>'T=>bool)) %% \ 
13404  86 
\ (meta_eq_to_obj_eq % TYPE('T) % A % B %% prf1)) %% \ 
87 
\ (meta_eq_to_obj_eq % TYPE('T) % C % D %% prf2)) %% \ 

88 
\ (meta_eq_to_obj_eq % TYPE('T) % C % D %% prf3))", 

89 

90 
(** rewriting on bool: insert proper congruence rules for logical connectives **) 

91 

92 
(* All *) 

93 

94 
"(iffD1 % All P % All Q %% (cong % TYPE('T1) % TYPE('T2) % All % All % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

95 
\ (HOL.refl % TYPE('T3) % x1) %% (ext % TYPE(bool) % TYPE('a) % x2 % x3 %% prf)) %% prf') == \ 
13404  96 
\ (allI % TYPE('a) % Q %% \ 
97 
\ (Lam x. \ 

98 
\ iffD1 % P x % Q x %% (prf % x) %% \ 

99 
\ (spec % TYPE('a) % P % x %% prf')))", 

100 

101 
"(iffD2 % All P % All Q %% (cong % TYPE('T1) % TYPE('T2) % All % All % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

102 
\ (HOL.refl % TYPE('T3) % x1) %% (ext % TYPE(bool) % TYPE('a) % x2 % x3 %% prf)) %% prf') == \ 
13404  103 
\ (allI % TYPE('a) % P %% \ 
104 
\ (Lam x. \ 

105 
\ iffD2 % P x % Q x %% (prf % x) %% \ 

19798  106 
\ (spec % TYPE('a) % Q % x %% prf')))", 
13404  107 

108 
(* Ex *) 

109 

110 
"(iffD1 % Ex P % Ex Q %% (cong % TYPE('T1) % TYPE('T2) % Ex % Ex % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

111 
\ (HOL.refl % TYPE('T3) % x1) %% (ext % TYPE(bool) % TYPE('a) % x2 % x3 %% prf)) %% prf') == \ 
13404  112 
\ (exE % TYPE('a) % P % EX x. Q x %% prf' %% \ 
113 
\ (Lam x H : P x. \ 

114 
\ exI % TYPE('a) % Q % x %% \ 

115 
\ (iffD1 % P x % Q x %% (prf % x) %% H)))", 

116 

117 
"(iffD2 % Ex P % Ex Q %% (cong % TYPE('T1) % TYPE('T2) % Ex % Ex % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

118 
\ (HOL.refl % TYPE('T3) % x1) %% (ext % TYPE(bool) % TYPE('a) % x2 % x3 %% prf)) %% prf') == \ 
13404  119 
\ (exE % TYPE('a) % Q % EX x. P x %% prf' %% \ 
120 
\ (Lam x H : Q x. \ 

121 
\ exI % TYPE('a) % P % x %% \ 

122 
\ (iffD2 % P x % Q x %% (prf % x) %% H)))", 

123 

124 
(* & *) 

125 

126 
"(iffD1 % A & C % B & D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

127 
\ (cong % TYPE('T3) % TYPE('T4) % op & % op & % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

128 
\ (HOL.refl % TYPE('T5) % op &) %% prf1) %% prf2) %% prf3) == \ 
13404  129 
\ (conjI % B % D %% \ 
130 
\ (iffD1 % A % B %% prf1 %% (conjunct1 % A % C %% prf3)) %% \ 

131 
\ (iffD1 % C % D %% prf2 %% (conjunct2 % A % C %% prf3)))", 

132 

133 
"(iffD2 % A & C % B & D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

134 
\ (cong % TYPE('T3) % TYPE('T4) % op & % op & % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

135 
\ (HOL.refl % TYPE('T5) % op &) %% prf1) %% prf2) %% prf3) == \ 
13404  136 
\ (conjI % A % C %% \ 
137 
\ (iffD2 % A % B %% prf1 %% (conjunct1 % B % D %% prf3)) %% \ 

138 
\ (iffD2 % C % D %% prf2 %% (conjunct2 % B % D %% prf3)))", 

139 

13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

140 
"(cong % TYPE(bool) % TYPE(bool) % op & A % op & A % B % C %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

141 
\ (HOL.refl % TYPE(bool=>bool) % op & A)) == \ 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

142 
\ (cong % TYPE(bool) % TYPE(bool) % op & A % op & A % B % C %% \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

143 
\ (cong % TYPE(bool=>bool) % TYPE(bool) % \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

144 
\ (op & :: bool=>bool=>bool) % (op & :: bool=>bool=>bool) % A % A %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

145 
\ (HOL.refl % TYPE(bool=>bool=>bool) % (op & :: bool=>bool=>bool)) %% \ 
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

146 
\ (HOL.refl % TYPE(bool) % A)))", 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

147 

13404  148 
(*  *) 
149 

150 
"(iffD1 % A  C % B  D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

151 
\ (cong % TYPE('T3) % TYPE('T4) % op  % op  % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

152 
\ (HOL.refl % TYPE('T5) % op  ) %% prf1) %% prf2) %% prf3) == \ 
13404  153 
\ (disjE % A % C % B  D %% prf3 %% \ 
154 
\ (Lam H : A. disjI1 % B % D %% (iffD1 % A % B %% prf1 %% H)) %% \ 

155 
\ (Lam H : C. disjI2 % D % B %% (iffD1 % C % D %% prf2 %% H)))", 

156 

157 
"(iffD2 % A  C % B  D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

158 
\ (cong % TYPE('T3) % TYPE('T4) % op  % op  % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

159 
\ (HOL.refl % TYPE('T5) % op  ) %% prf1) %% prf2) %% prf3) == \ 
13404  160 
\ (disjE % B % D % A  C %% prf3 %% \ 
161 
\ (Lam H : B. disjI1 % A % C %% (iffD2 % A % B %% prf1 %% H)) %% \ 

162 
\ (Lam H : D. disjI2 % C % A %% (iffD2 % C % D %% prf2 %% H)))", 

163 

13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

164 
"(cong % TYPE(bool) % TYPE(bool) % op  A % op  A % B % C %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

165 
\ (HOL.refl % TYPE(bool=>bool) % op  A)) == \ 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

166 
\ (cong % TYPE(bool) % TYPE(bool) % op  A % op  A % B % C %% \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

167 
\ (cong % TYPE(bool=>bool) % TYPE(bool) % \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

168 
\ (op  :: bool=>bool=>bool) % (op  :: bool=>bool=>bool) % A % A %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

169 
\ (HOL.refl % TYPE(bool=>bool=>bool) % (op  :: bool=>bool=>bool)) %% \ 
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

170 
\ (HOL.refl % TYPE(bool) % A)))", 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

171 

13404  172 
(* > *) 
173 

174 
"(iffD1 % A > C % B > D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

175 
\ (cong % TYPE('T3) % TYPE('T4) % op > % op > % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

176 
\ (HOL.refl % TYPE('T5) % op > ) %% prf1) %% prf2) %% prf3) == \ 
13404  177 
\ (impI % B % D %% (Lam H: B. iffD1 % C % D %% prf2 %% \ 
178 
\ (mp % A % C %% prf3 %% (iffD2 % A % B %% prf1 %% H))))", 

179 

180 
"(iffD2 % A > C % B > D %% (cong % TYPE('T1) % TYPE('T2) % x1 % x2 % C % D %% \ 

181 
\ (cong % TYPE('T3) % TYPE('T4) % op > % op > % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

182 
\ (HOL.refl % TYPE('T5) % op > ) %% prf1) %% prf2) %% prf3) == \ 
13404  183 
\ (impI % A % C %% (Lam H: A. iffD2 % C % D %% prf2 %% \ 
184 
\ (mp % B % D %% prf3 %% (iffD1 % A % B %% prf1 %% H))))", 

185 

13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

186 
"(cong % TYPE(bool) % TYPE(bool) % op > A % op > A % B % C %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

187 
\ (HOL.refl % TYPE(bool=>bool) % op > A)) == \ 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

188 
\ (cong % TYPE(bool) % TYPE(bool) % op > A % op > A % B % C %% \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

189 
\ (cong % TYPE(bool=>bool) % TYPE(bool) % \ 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

190 
\ (op > :: bool=>bool=>bool) % (op > :: bool=>bool=>bool) % A % A %% \ 
15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

191 
\ (HOL.refl % TYPE(bool=>bool=>bool) % (op > :: bool=>bool=>bool)) %% \ 
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

192 
\ (HOL.refl % TYPE(bool) % A)))", 
13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

193 

13404  194 
(* ~ *) 
195 

196 
"(iffD1 % ~ P % ~ Q %% (cong % TYPE('T1) % TYPE('T2) % Not % Not % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

197 
\ (HOL.refl % TYPE('T3) % Not) %% prf1) %% prf2) == \ 
13404  198 
\ (notI % Q %% (Lam H: Q. \ 
199 
\ notE % P % False %% prf2 %% (iffD2 % P % Q %% prf1 %% H)))", 

200 

201 
"(iffD2 % ~ P % ~ Q %% (cong % TYPE('T1) % TYPE('T2) % Not % Not % P % Q %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

202 
\ (HOL.refl % TYPE('T3) % Not) %% prf1) %% prf2) == \ 
13404  203 
\ (notI % P %% (Lam H: P. \ 
204 
\ notE % Q % False %% prf2 %% (iffD1 % P % Q %% prf1 %% H)))", 

205 

206 
(* = *) 

207 

208 
"(iffD1 % B % D %% \ 

209 
\ (iffD1 % A = C % B = D %% (cong % TYPE('T1) % TYPE(bool) % x1 % x2 % C % D %% \ 

210 
\ (cong % TYPE('T2) % TYPE(bool) % op = % op = % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

211 
\ (HOL.refl % TYPE('T3) % op =) %% prf1) %% prf2) %% prf3) %% prf4) == \ 
13404  212 
\ (iffD1 % C % D %% prf2 %% \ 
213 
\ (iffD1 % A % C %% prf3 %% (iffD2 % A % B %% prf1 %% prf4)))", 

214 

215 
"(iffD2 % B % D %% \ 

216 
\ (iffD1 % A = C % B = D %% (cong % TYPE('T1) % TYPE(bool) % x1 % x2 % C % D %% \ 

217 
\ (cong % TYPE('T2) % TYPE(bool) % op = % op = % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

218 
\ (HOL.refl % TYPE('T3) % op =) %% prf1) %% prf2) %% prf3) %% prf4) == \ 
13404  219 
\ (iffD1 % A % B %% prf1 %% \ 
220 
\ (iffD2 % A % C %% prf3 %% (iffD2 % C % D %% prf2 %% prf4)))", 

221 

222 
"(iffD1 % A % C %% \ 

223 
\ (iffD2 % A = C % B = D %% (cong % TYPE('T1) % TYPE(bool) % x1 % x2 % C % D %% \ 

224 
\ (cong % TYPE('T2) % TYPE(bool) % op = % op = % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

225 
\ (HOL.refl % TYPE('T3) % op =) %% prf1) %% prf2) %% prf3) %% prf4)== \ 
13404  226 
\ (iffD2 % C % D %% prf2 %% \ 
227 
\ (iffD1 % B % D %% prf3 %% (iffD1 % A % B %% prf1 %% prf4)))", 

228 

229 
"(iffD2 % A % C %% \ 

230 
\ (iffD2 % A = C % B = D %% (cong % TYPE('T1) % TYPE(bool) % x1 % x2 % C % D %% \ 

231 
\ (cong % TYPE('T2) % TYPE(bool) % op = % op = % A % B %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

232 
\ (HOL.refl % TYPE('T3) % op =) %% prf1) %% prf2) %% prf3) %% prf4) == \ 
13404  233 
\ (iffD2 % A % B %% prf1 %% \ 
234 
\ (iffD2 % B % D %% prf3 %% (iffD1 % C % D %% prf2 %% prf4)))", 

235 

236 
"(cong % TYPE(bool) % TYPE(bool) % op = A % op = A % B % C %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

237 
\ (HOL.refl % TYPE(bool=>bool) % op = A)) == \ 
13404  238 
\ (cong % TYPE(bool) % TYPE(bool) % op = A % op = A % B % C %% \ 
239 
\ (cong % TYPE(bool=>bool) % TYPE(bool) % \ 

240 
\ (op = :: bool=>bool=>bool) % (op = :: bool=>bool=>bool) % A % A %% \ 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

241 
\ (HOL.refl % TYPE(bool=>bool=>bool) % (op = :: bool=>bool=>bool)) %% \ 
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

242 
\ (HOL.refl % TYPE(bool) % A)))", 
13404  243 

13916
f078a758e5d8
elim_cong now etaexpands proofs on the fly if required.
berghofe
parents:
13602
diff
changeset

244 
(** transitivity, reflexivity, and symmetry **) 
f078a758e5d8
elim_cong now etaexpands proofs on the fly if required.
berghofe
parents:
13602
diff
changeset

245 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

246 
"(iffD1 % A % C %% (HOL.trans % TYPE(bool) % A % B % C %% prf1 %% prf2) %% prf3) == \ 
13404  247 
\ (iffD1 % B % C %% prf2 %% (iffD1 % A % B %% prf1 %% prf3))", 
248 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

249 
"(iffD2 % A % C %% (HOL.trans % TYPE(bool) % A % B % C %% prf1 %% prf2) %% prf3) == \ 
13404  250 
\ (iffD2 % A % B %% prf1 %% (iffD2 % B % C %% prf2 %% prf3))", 
251 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

252 
"(iffD1 % A % A %% (HOL.refl % TYPE(bool) % A) %% prf) == prf", 
13404  253 

15530
6f43714517ee
Fully qualified refl and trans to avoid confusion with theorems
berghofe
parents:
14981
diff
changeset

254 
"(iffD2 % A % A %% (HOL.refl % TYPE(bool) % A) %% prf) == prf", 
13404  255 

13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

256 
"(iffD1 % A % B %% (sym % TYPE(bool) % B % A %% prf)) == (iffD2 % B % A %% prf)", 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

257 

4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

258 
"(iffD2 % A % B %% (sym % TYPE(bool) % B % A %% prf)) == (iffD1 % B % A %% prf)", 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

259 

13404  260 
(** normalization of HOL proofs **) 
261 

262 
"(mp % A % B %% (impI % A % B %% prf)) == prf", 

263 

264 
"(impI % A % B %% (mp % A % B %% prf)) == prf", 

265 

266 
"(spec % TYPE('a) % P % x %% (allI % TYPE('a) % P %% prf)) == prf % x", 

267 

268 
"(allI % TYPE('a) % P %% (Lam x::'a. spec % TYPE('a) % P % x %% prf)) == prf", 

269 

13602
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

270 
"(exE % TYPE('a) % P % Q %% (exI % TYPE('a) % P % x %% prf1) %% prf2) == (prf2 % x %% prf1)", 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

271 

4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

272 
"(exE % TYPE('a) % P % Q %% prf %% (exI % TYPE('a) % P)) == prf", 
4cecd1e0f4a9
 additional congruence rules for boolean operators
berghofe
parents:
13404
diff
changeset

273 

13404  274 
"(disjE % P % Q % R %% (disjI1 % P % Q %% prf1) %% prf2 %% prf3) == (prf2 %% prf1)", 
275 

276 
"(disjE % P % Q % R %% (disjI2 % Q % P %% prf1) %% prf2 %% prf3) == (prf3 %% prf1)", 

277 

278 
"(conjunct1 % P % Q %% (conjI % P % Q %% prf1 %% prf2)) == prf1", 

279 

280 
"(conjunct2 % P % Q %% (conjI % P % Q %% prf1 %% prf2)) == prf2", 

281 

282 
"(iffD1 % A % B %% (iffI % A % B %% prf1 %% prf2)) == prf1", 

283 

284 
"(iffD2 % A % B %% (iffI % A % B %% prf1 %% prf2)) == prf2"]; 

285 

286 

287 
(** Replace congruence rules by substitution rules **) 

288 

28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

289 
fun strip_cong ps (PThm (_, (("HOL.cong", _, _), _)) % _ % _ % SOME x % SOME y %% 
13404  290 
prf1 %% prf2) = strip_cong (((x, y), prf2) :: ps) prf1 
28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

291 
 strip_cong ps (PThm (_, (("HOL.refl", _, _), _)) % SOME f) = SOME (f, ps) 
15531  292 
 strip_cong _ _ = NONE; 
13404  293 

28814  294 
val subst_prf = fst (strip_combt (Thm.proof_of subst)); 
295 
val sym_prf = fst (strip_combt (Thm.proof_of sym)); 

13404  296 

297 
fun make_subst Ts prf xs (_, []) = prf 

298 
 make_subst Ts prf xs (f, ((x, y), prf') :: ps) = 

299 
let val T = fastype_of1 (Ts, x) 

300 
in if x aconv y then make_subst Ts prf (xs @ [x]) (f, ps) 

15531  301 
else change_type (SOME [T]) subst_prf %> x %> y %> 
13404  302 
Abs ("z", T, list_comb (incr_boundvars 1 f, 
303 
map (incr_boundvars 1) xs @ Bound 0 :: 

304 
map (incr_boundvars 1 o snd o fst) ps)) %% prf' %% 

305 
make_subst Ts prf (xs @ [x]) (f, ps) 

306 
end; 

307 

308 
fun make_sym Ts ((x, y), prf) = 

15531  309 
((y, x), change_type (SOME [fastype_of1 (Ts, x)]) sym_prf %> x %> y %% prf); 
13404  310 

22277  311 
fun mk_AbsP P t = AbsP ("H", Option.map HOLogic.mk_Trueprop P, t); 
13916
f078a758e5d8
elim_cong now etaexpands proofs on the fly if required.
berghofe
parents:
13602
diff
changeset

312 

28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

313 
fun elim_cong Ts (PThm (_, (("HOL.iffD1", _, _), _)) % _ % _ %% prf1 %% prf2) = 
15570  314 
Option.map (make_subst Ts prf2 []) (strip_cong [] prf1) 
28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

315 
 elim_cong Ts (PThm (_, (("HOL.iffD1", _, _), _)) % P % _ %% prf) = 
15570  316 
Option.map (mk_AbsP P o make_subst Ts (PBound 0) []) 
13916
f078a758e5d8
elim_cong now etaexpands proofs on the fly if required.
berghofe
parents:
13602
diff
changeset

317 
(strip_cong [] (incr_pboundvars 1 0 prf)) 
28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

318 
 elim_cong Ts (PThm (_, (("HOL.iffD2", _, _), _)) % _ % _ %% prf1 %% prf2) = 
15570  319 
Option.map (make_subst Ts prf2 [] o 
13404  320 
apsnd (map (make_sym Ts))) (strip_cong [] prf1) 
28801
fc45401bdf6f
ProofSyntax.proof_of_term: removed obsolete disambiguisation table;
wenzelm
parents:
28712
diff
changeset

321 
 elim_cong Ts (PThm (_, (("HOL.iffD2", _, _), _)) % _ % P %% prf) = 
15570  322 
Option.map (mk_AbsP P o make_subst Ts (PBound 0) [] o 
13916
f078a758e5d8
elim_cong now etaexpands proofs on the fly if required.
berghofe
parents:
13602
diff
changeset

323 
apsnd (map (make_sym Ts))) (strip_cong [] (incr_pboundvars 1 0 prf)) 
15531  324 
 elim_cong _ _ = NONE; 
13404  325 

326 
end; 