1.1 --- a/src/HOL/Extraction.thy Sun Jun 30 09:26:00 2013 +0200
1.2 +++ b/src/HOL/Extraction.thy Sun Jun 30 11:30:16 2013 +0200
1.3 @@ -203,209 +203,209 @@
1.4
1.5 realizers
1.6 impI (P, Q): "\<lambda>pq. pq"
1.7 - "\<Lambda> (c: _) (d: _) P Q pq (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h \<cdot> x))"
1.8 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h \<cdot> x))"
1.9
1.10 impI (P): "Null"
1.11 - "\<Lambda> (c: _) P Q (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h \<cdot> x))"
1.12 + "\<^bold>\<lambda>(c: _) P Q (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h \<cdot> x))"
1.13
1.14 - impI (Q): "\<lambda>q. q" "\<Lambda> (c: _) P Q q. impI \<cdot> _ \<cdot> _"
1.15 + impI (Q): "\<lambda>q. q" "\<^bold>\<lambda>(c: _) P Q q. impI \<cdot> _ \<cdot> _"
1.16
1.17 impI: "Null" "impI"
1.18
1.19 mp (P, Q): "\<lambda>pq. pq"
1.20 - "\<Lambda> (c: _) (d: _) P Q pq (h: _) p. mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.21 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq (h: _) p. mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.22
1.23 mp (P): "Null"
1.24 - "\<Lambda> (c: _) P Q (h: _) p. mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.25 + "\<^bold>\<lambda>(c: _) P Q (h: _) p. mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.26
1.27 - mp (Q): "\<lambda>q. q" "\<Lambda> (c: _) P Q q. mp \<cdot> _ \<cdot> _"
1.28 + mp (Q): "\<lambda>q. q" "\<^bold>\<lambda>(c: _) P Q q. mp \<cdot> _ \<cdot> _"
1.29
1.30 mp: "Null" "mp"
1.31
1.32 - allI (P): "\<lambda>p. p" "\<Lambda> (c: _) P (d: _) p. allI \<cdot> _ \<bullet> d"
1.33 + allI (P): "\<lambda>p. p" "\<^bold>\<lambda>(c: _) P (d: _) p. allI \<cdot> _ \<bullet> d"
1.34
1.35 allI: "Null" "allI"
1.36
1.37 - spec (P): "\<lambda>x p. p x" "\<Lambda> (c: _) P x (d: _) p. spec \<cdot> _ \<cdot> x \<bullet> d"
1.38 + spec (P): "\<lambda>x p. p x" "\<^bold>\<lambda>(c: _) P x (d: _) p. spec \<cdot> _ \<cdot> x \<bullet> d"
1.39
1.40 spec: "Null" "spec"
1.41
1.42 - exI (P): "\<lambda>x p. (x, p)" "\<Lambda> (c: _) P x (d: _) p. exI_realizer \<cdot> P \<cdot> p \<cdot> x \<bullet> c \<bullet> d"
1.43 + exI (P): "\<lambda>x p. (x, p)" "\<^bold>\<lambda>(c: _) P x (d: _) p. exI_realizer \<cdot> P \<cdot> p \<cdot> x \<bullet> c \<bullet> d"
1.44
1.45 - exI: "\<lambda>x. x" "\<Lambda> P x (c: _) (h: _). h"
1.46 + exI: "\<lambda>x. x" "\<^bold>\<lambda>P x (c: _) (h: _). h"
1.47
1.48 exE (P, Q): "\<lambda>p pq. let (x, y) = p in pq x y"
1.49 - "\<Lambda> (c: _) (d: _) P Q (e: _) p (h: _) pq. exE_realizer \<cdot> P \<cdot> p \<cdot> Q \<cdot> pq \<bullet> c \<bullet> e \<bullet> d \<bullet> h"
1.50 + "\<^bold>\<lambda>(c: _) (d: _) P Q (e: _) p (h: _) pq. exE_realizer \<cdot> P \<cdot> p \<cdot> Q \<cdot> pq \<bullet> c \<bullet> e \<bullet> d \<bullet> h"
1.51
1.52 exE (P): "Null"
1.53 - "\<Lambda> (c: _) P Q (d: _) p. exE_realizer' \<cdot> _ \<cdot> _ \<cdot> _ \<bullet> c \<bullet> d"
1.54 + "\<^bold>\<lambda>(c: _) P Q (d: _) p. exE_realizer' \<cdot> _ \<cdot> _ \<cdot> _ \<bullet> c \<bullet> d"
1.55
1.56 exE (Q): "\<lambda>x pq. pq x"
1.57 - "\<Lambda> (c: _) P Q (d: _) x (h1: _) pq (h2: _). h2 \<cdot> x \<bullet> h1"
1.58 + "\<^bold>\<lambda>(c: _) P Q (d: _) x (h1: _) pq (h2: _). h2 \<cdot> x \<bullet> h1"
1.59
1.60 exE: "Null"
1.61 - "\<Lambda> P Q (c: _) x (h1: _) (h2: _). h2 \<cdot> x \<bullet> h1"
1.62 + "\<^bold>\<lambda>P Q (c: _) x (h1: _) (h2: _). h2 \<cdot> x \<bullet> h1"
1.63
1.64 conjI (P, Q): "Pair"
1.65 - "\<Lambda> (c: _) (d: _) P Q p (h: _) q. conjI_realizer \<cdot> P \<cdot> p \<cdot> Q \<cdot> q \<bullet> c \<bullet> d \<bullet> h"
1.66 + "\<^bold>\<lambda>(c: _) (d: _) P Q p (h: _) q. conjI_realizer \<cdot> P \<cdot> p \<cdot> Q \<cdot> q \<bullet> c \<bullet> d \<bullet> h"
1.67
1.68 conjI (P): "\<lambda>p. p"
1.69 - "\<Lambda> (c: _) P Q p. conjI \<cdot> _ \<cdot> _"
1.70 + "\<^bold>\<lambda>(c: _) P Q p. conjI \<cdot> _ \<cdot> _"
1.71
1.72 conjI (Q): "\<lambda>q. q"
1.73 - "\<Lambda> (c: _) P Q (h: _) q. conjI \<cdot> _ \<cdot> _ \<bullet> h"
1.74 + "\<^bold>\<lambda>(c: _) P Q (h: _) q. conjI \<cdot> _ \<cdot> _ \<bullet> h"
1.75
1.76 conjI: "Null" "conjI"
1.77
1.78 conjunct1 (P, Q): "fst"
1.79 - "\<Lambda> (c: _) (d: _) P Q pq. conjunct1 \<cdot> _ \<cdot> _"
1.80 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq. conjunct1 \<cdot> _ \<cdot> _"
1.81
1.82 conjunct1 (P): "\<lambda>p. p"
1.83 - "\<Lambda> (c: _) P Q p. conjunct1 \<cdot> _ \<cdot> _"
1.84 + "\<^bold>\<lambda>(c: _) P Q p. conjunct1 \<cdot> _ \<cdot> _"
1.85
1.86 conjunct1 (Q): "Null"
1.87 - "\<Lambda> (c: _) P Q q. conjunct1 \<cdot> _ \<cdot> _"
1.88 + "\<^bold>\<lambda>(c: _) P Q q. conjunct1 \<cdot> _ \<cdot> _"
1.89
1.90 conjunct1: "Null" "conjunct1"
1.91
1.92 conjunct2 (P, Q): "snd"
1.93 - "\<Lambda> (c: _) (d: _) P Q pq. conjunct2 \<cdot> _ \<cdot> _"
1.94 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq. conjunct2 \<cdot> _ \<cdot> _"
1.95
1.96 conjunct2 (P): "Null"
1.97 - "\<Lambda> (c: _) P Q p. conjunct2 \<cdot> _ \<cdot> _"
1.98 + "\<^bold>\<lambda>(c: _) P Q p. conjunct2 \<cdot> _ \<cdot> _"
1.99
1.100 conjunct2 (Q): "\<lambda>p. p"
1.101 - "\<Lambda> (c: _) P Q p. conjunct2 \<cdot> _ \<cdot> _"
1.102 + "\<^bold>\<lambda>(c: _) P Q p. conjunct2 \<cdot> _ \<cdot> _"
1.103
1.104 conjunct2: "Null" "conjunct2"
1.105
1.106 disjI1 (P, Q): "Inl"
1.107 - "\<Lambda> (c: _) (d: _) P Q p. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sum.cases_1 \<cdot> P \<cdot> _ \<cdot> p \<bullet> arity_type_bool \<bullet> c \<bullet> d)"
1.108 + "\<^bold>\<lambda>(c: _) (d: _) P Q p. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sum.cases_1 \<cdot> P \<cdot> _ \<cdot> p \<bullet> arity_type_bool \<bullet> c \<bullet> d)"
1.109
1.110 disjI1 (P): "Some"
1.111 - "\<Lambda> (c: _) P Q p. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_2 \<cdot> _ \<cdot> P \<cdot> p \<bullet> arity_type_bool \<bullet> c)"
1.112 + "\<^bold>\<lambda>(c: _) P Q p. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_2 \<cdot> _ \<cdot> P \<cdot> p \<bullet> arity_type_bool \<bullet> c)"
1.113
1.114 disjI1 (Q): "None"
1.115 - "\<Lambda> (c: _) P Q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool \<bullet> c)"
1.116 + "\<^bold>\<lambda>(c: _) P Q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool \<bullet> c)"
1.117
1.118 disjI1: "Left"
1.119 - "\<Lambda> P Q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sumbool.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool)"
1.120 + "\<^bold>\<lambda>P Q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sumbool.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool)"
1.121
1.122 disjI2 (P, Q): "Inr"
1.123 - "\<Lambda> (d: _) (c: _) Q P q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sum.cases_2 \<cdot> _ \<cdot> Q \<cdot> q \<bullet> arity_type_bool \<bullet> c \<bullet> d)"
1.124 + "\<^bold>\<lambda>(d: _) (c: _) Q P q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sum.cases_2 \<cdot> _ \<cdot> Q \<cdot> q \<bullet> arity_type_bool \<bullet> c \<bullet> d)"
1.125
1.126 disjI2 (P): "None"
1.127 - "\<Lambda> (c: _) Q P. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool \<bullet> c)"
1.128 + "\<^bold>\<lambda>(c: _) Q P. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_1 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool \<bullet> c)"
1.129
1.130 disjI2 (Q): "Some"
1.131 - "\<Lambda> (c: _) Q P q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_2 \<cdot> _ \<cdot> Q \<cdot> q \<bullet> arity_type_bool \<bullet> c)"
1.132 + "\<^bold>\<lambda>(c: _) Q P q. iffD2 \<cdot> _ \<cdot> _ \<bullet> (option.cases_2 \<cdot> _ \<cdot> Q \<cdot> q \<bullet> arity_type_bool \<bullet> c)"
1.133
1.134 disjI2: "Right"
1.135 - "\<Lambda> Q P. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sumbool.cases_2 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool)"
1.136 + "\<^bold>\<lambda>Q P. iffD2 \<cdot> _ \<cdot> _ \<bullet> (sumbool.cases_2 \<cdot> _ \<cdot> _ \<bullet> arity_type_bool)"
1.137
1.138 disjE (P, Q, R): "\<lambda>pq pr qr.
1.139 (case pq of Inl p \<Rightarrow> pr p | Inr q \<Rightarrow> qr q)"
1.140 - "\<Lambda> (c: _) (d: _) (e: _) P Q R pq (h1: _) pr (h2: _) qr.
1.141 + "\<^bold>\<lambda>(c: _) (d: _) (e: _) P Q R pq (h1: _) pr (h2: _) qr.
1.142 disjE_realizer \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> R \<cdot> pr \<cdot> qr \<bullet> c \<bullet> d \<bullet> e \<bullet> h1 \<bullet> h2"
1.143
1.144 disjE (Q, R): "\<lambda>pq pr qr.
1.145 (case pq of None \<Rightarrow> pr | Some q \<Rightarrow> qr q)"
1.146 - "\<Lambda> (c: _) (d: _) P Q R pq (h1: _) pr (h2: _) qr.
1.147 + "\<^bold>\<lambda>(c: _) (d: _) P Q R pq (h1: _) pr (h2: _) qr.
1.148 disjE_realizer2 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> R \<cdot> pr \<cdot> qr \<bullet> c \<bullet> d \<bullet> h1 \<bullet> h2"
1.149
1.150 disjE (P, R): "\<lambda>pq pr qr.
1.151 (case pq of None \<Rightarrow> qr | Some p \<Rightarrow> pr p)"
1.152 - "\<Lambda> (c: _) (d: _) P Q R pq (h1: _) pr (h2: _) qr (h3: _).
1.153 + "\<^bold>\<lambda>(c: _) (d: _) P Q R pq (h1: _) pr (h2: _) qr (h3: _).
1.154 disjE_realizer2 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> R \<cdot> qr \<cdot> pr \<bullet> c \<bullet> d \<bullet> h1 \<bullet> h3 \<bullet> h2"
1.155
1.156 disjE (R): "\<lambda>pq pr qr.
1.157 (case pq of Left \<Rightarrow> pr | Right \<Rightarrow> qr)"
1.158 - "\<Lambda> (c: _) P Q R pq (h1: _) pr (h2: _) qr.
1.159 + "\<^bold>\<lambda>(c: _) P Q R pq (h1: _) pr (h2: _) qr.
1.160 disjE_realizer3 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> R \<cdot> pr \<cdot> qr \<bullet> c \<bullet> h1 \<bullet> h2"
1.161
1.162 disjE (P, Q): "Null"
1.163 - "\<Lambda> (c: _) (d: _) P Q R pq. disjE_realizer \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> c \<bullet> d \<bullet> arity_type_bool"
1.164 + "\<^bold>\<lambda>(c: _) (d: _) P Q R pq. disjE_realizer \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> c \<bullet> d \<bullet> arity_type_bool"
1.165
1.166 disjE (Q): "Null"
1.167 - "\<Lambda> (c: _) P Q R pq. disjE_realizer2 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> c \<bullet> arity_type_bool"
1.168 + "\<^bold>\<lambda>(c: _) P Q R pq. disjE_realizer2 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> c \<bullet> arity_type_bool"
1.169
1.170 disjE (P): "Null"
1.171 - "\<Lambda> (c: _) P Q R pq (h1: _) (h2: _) (h3: _).
1.172 + "\<^bold>\<lambda>(c: _) P Q R pq (h1: _) (h2: _) (h3: _).
1.173 disjE_realizer2 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> c \<bullet> arity_type_bool \<bullet> h1 \<bullet> h3 \<bullet> h2"
1.174
1.175 disjE: "Null"
1.176 - "\<Lambda> P Q R pq. disjE_realizer3 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> arity_type_bool"
1.177 + "\<^bold>\<lambda>P Q R pq. disjE_realizer3 \<cdot> _ \<cdot> _ \<cdot> pq \<cdot> (\<lambda>x. R) \<cdot> _ \<cdot> _ \<bullet> arity_type_bool"
1.178
1.179 FalseE (P): "default"
1.180 - "\<Lambda> (c: _) P. FalseE \<cdot> _"
1.181 + "\<^bold>\<lambda>(c: _) P. FalseE \<cdot> _"
1.182
1.183 FalseE: "Null" "FalseE"
1.184
1.185 notI (P): "Null"
1.186 - "\<Lambda> (c: _) P (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. notI \<cdot> _ \<bullet> (h \<cdot> x))"
1.187 + "\<^bold>\<lambda>(c: _) P (h: _). allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. notI \<cdot> _ \<bullet> (h \<cdot> x))"
1.188
1.189 notI: "Null" "notI"
1.190
1.191 notE (P, R): "\<lambda>p. default"
1.192 - "\<Lambda> (c: _) (d: _) P R (h: _) p. notE \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.193 + "\<^bold>\<lambda>(c: _) (d: _) P R (h: _) p. notE \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.194
1.195 notE (P): "Null"
1.196 - "\<Lambda> (c: _) P R (h: _) p. notE \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.197 + "\<^bold>\<lambda>(c: _) P R (h: _) p. notE \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> c \<bullet> h)"
1.198
1.199 notE (R): "default"
1.200 - "\<Lambda> (c: _) P R. notE \<cdot> _ \<cdot> _"
1.201 + "\<^bold>\<lambda>(c: _) P R. notE \<cdot> _ \<cdot> _"
1.202
1.203 notE: "Null" "notE"
1.204
1.205 subst (P): "\<lambda>s t ps. ps"
1.206 - "\<Lambda> (c: _) s t P (d: _) (h: _) ps. subst \<cdot> s \<cdot> t \<cdot> P ps \<bullet> d \<bullet> h"
1.207 + "\<^bold>\<lambda>(c: _) s t P (d: _) (h: _) ps. subst \<cdot> s \<cdot> t \<cdot> P ps \<bullet> d \<bullet> h"
1.208
1.209 subst: "Null" "subst"
1.210
1.211 iffD1 (P, Q): "fst"
1.212 - "\<Lambda> (d: _) (c: _) Q P pq (h: _) p.
1.213 + "\<^bold>\<lambda>(d: _) (c: _) Q P pq (h: _) p.
1.214 mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> p \<bullet> d \<bullet> (conjunct1 \<cdot> _ \<cdot> _ \<bullet> h))"
1.215
1.216 iffD1 (P): "\<lambda>p. p"
1.217 - "\<Lambda> (c: _) Q P p (h: _). mp \<cdot> _ \<cdot> _ \<bullet> (conjunct1 \<cdot> _ \<cdot> _ \<bullet> h)"
1.218 + "\<^bold>\<lambda>(c: _) Q P p (h: _). mp \<cdot> _ \<cdot> _ \<bullet> (conjunct1 \<cdot> _ \<cdot> _ \<bullet> h)"
1.219
1.220 iffD1 (Q): "Null"
1.221 - "\<Lambda> (c: _) Q P q1 (h: _) q2.
1.222 + "\<^bold>\<lambda>(c: _) Q P q1 (h: _) q2.
1.223 mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> q2 \<bullet> c \<bullet> (conjunct1 \<cdot> _ \<cdot> _ \<bullet> h))"
1.224
1.225 iffD1: "Null" "iffD1"
1.226
1.227 iffD2 (P, Q): "snd"
1.228 - "\<Lambda> (c: _) (d: _) P Q pq (h: _) q.
1.229 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq (h: _) q.
1.230 mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> q \<bullet> d \<bullet> (conjunct2 \<cdot> _ \<cdot> _ \<bullet> h))"
1.231
1.232 iffD2 (P): "\<lambda>p. p"
1.233 - "\<Lambda> (c: _) P Q p (h: _). mp \<cdot> _ \<cdot> _ \<bullet> (conjunct2 \<cdot> _ \<cdot> _ \<bullet> h)"
1.234 + "\<^bold>\<lambda>(c: _) P Q p (h: _). mp \<cdot> _ \<cdot> _ \<bullet> (conjunct2 \<cdot> _ \<cdot> _ \<bullet> h)"
1.235
1.236 iffD2 (Q): "Null"
1.237 - "\<Lambda> (c: _) P Q q1 (h: _) q2.
1.238 + "\<^bold>\<lambda>(c: _) P Q q1 (h: _) q2.
1.239 mp \<cdot> _ \<cdot> _ \<bullet> (spec \<cdot> _ \<cdot> q2 \<bullet> c \<bullet> (conjunct2 \<cdot> _ \<cdot> _ \<bullet> h))"
1.240
1.241 iffD2: "Null" "iffD2"
1.242
1.243 iffI (P, Q): "Pair"
1.244 - "\<Lambda> (c: _) (d: _) P Q pq (h1 : _) qp (h2 : _). conjI_realizer \<cdot>
1.245 + "\<^bold>\<lambda>(c: _) (d: _) P Q pq (h1 : _) qp (h2 : _). conjI_realizer \<cdot>
1.246 (\<lambda>pq. \<forall>x. P x \<longrightarrow> Q (pq x)) \<cdot> pq \<cdot>
1.247 (\<lambda>qp. \<forall>x. Q x \<longrightarrow> P (qp x)) \<cdot> qp \<bullet>
1.248 (arity_type_fun \<bullet> c \<bullet> d) \<bullet>
1.249 (arity_type_fun \<bullet> d \<bullet> c) \<bullet>
1.250 - (allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h1 \<cdot> x))) \<bullet>
1.251 - (allI \<cdot> _ \<bullet> d \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h2 \<cdot> x)))"
1.252 + (allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h1 \<cdot> x))) \<bullet>
1.253 + (allI \<cdot> _ \<bullet> d \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h2 \<cdot> x)))"
1.254
1.255 iffI (P): "\<lambda>p. p"
1.256 - "\<Lambda> (c: _) P Q (h1 : _) p (h2 : _). conjI \<cdot> _ \<cdot> _ \<bullet>
1.257 - (allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h1 \<cdot> x))) \<bullet>
1.258 + "\<^bold>\<lambda>(c: _) P Q (h1 : _) p (h2 : _). conjI \<cdot> _ \<cdot> _ \<bullet>
1.259 + (allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h1 \<cdot> x))) \<bullet>
1.260 (impI \<cdot> _ \<cdot> _ \<bullet> h2)"
1.261
1.262 iffI (Q): "\<lambda>q. q"
1.263 - "\<Lambda> (c: _) P Q q (h1 : _) (h2 : _). conjI \<cdot> _ \<cdot> _ \<bullet>
1.264 + "\<^bold>\<lambda>(c: _) P Q q (h1 : _) (h2 : _). conjI \<cdot> _ \<cdot> _ \<bullet>
1.265 (impI \<cdot> _ \<cdot> _ \<bullet> h1) \<bullet>
1.266 - (allI \<cdot> _ \<bullet> c \<bullet> (\<Lambda> x. impI \<cdot> _ \<cdot> _ \<bullet> (h2 \<cdot> x)))"
1.267 + (allI \<cdot> _ \<bullet> c \<bullet> (\<^bold>\<lambda>x. impI \<cdot> _ \<cdot> _ \<bullet> (h2 \<cdot> x)))"
1.268
1.269 iffI: "Null" "iffI"
1.270