# HG changeset patch # User berghofe # Date 1004116013 -7200 # Node ID 9bd6e8e62a0661f5f7aa85c407723fe1d86dd32d # Parent 38e20c036e375e7f81b90b1fb1d037c83489d7da Eliminated occurrence of rule_format. diff -r 38e20c036e37 -r 9bd6e8e62a06 src/HOL/Lambda/Type.thy --- a/src/HOL/Lambda/Type.thy Fri Oct 26 18:16:45 2001 +0200 +++ b/src/HOL/Lambda/Type.thy Fri Oct 26 19:06:53 2001 +0200 @@ -93,7 +93,7 @@ by force -subsection {* @{text n}-ary function types *} +subsection {* n-ary function types *} lemma list_app_typeD [rule_format]: "\t T. e \ t \<^sub>\\<^sub>\ ts : T \ (\Ts. e \ t : Ts \ T \ e \ ts : Ts)" @@ -193,7 +193,7 @@ qed lemma lift_typings [rule_format]: - "\Ts. e \ ts : Ts \ (e\i:U\) \ (map (\t. lift t i) ts) : Ts" + "\Ts. e \ ts : Ts \ e\i:U\ \ (map (\t. lift t i) ts) : Ts" apply (induct_tac ts) apply simp apply (intro strip) @@ -214,7 +214,7 @@ done lemma substs_lemma [rule_format]: - "e \ u : T \ \Ts. (e\i:T\) \ ts : Ts \ + "e \ u : T \ \Ts. e\i:T\ \ ts : Ts \ e \ (map (\t. t[u/i]) ts) : Ts" apply (induct_tac ts) apply (intro strip) @@ -370,7 +370,6 @@ from varT True have T: "T = T'' \ Ts \ T'" by cases auto with uT have uT': "e \ u : T'' \ Ts \ T'" by simp - from Var have SI: "?R a" by cases (simp_all add: Cons) from T have "(Var 0 \<^sub>\\<^sub>\ map (\t. lift t 0) (map (\t. t[u/i]) as))[(u \<^sub>\ a[u/i])/0] \ IT" proof (rule MI2) @@ -385,8 +384,8 @@ show "e\0:T''\ \ Var 0 : T''" by (rule typing.Var) simp qed - from argT uIT uT show "a[u/i] \ IT" - by (rule SI[rule_format]) + from Var have "?R a" by cases (simp_all add: Cons) + with argT uIT uT show "a[u/i] \ IT" by simp from argT uT show "e \ a[u/i] : T''" by (rule subst_lemma) simp qed