(* Title: HOL/Library/Rewrite.thy
Author: Christoph Traut, Lars Noschinski, TU Muenchen
Proof method "rewrite" with support for subterm-selection based on patterns.
*)
theory Rewrite
imports Main
begin
consts rewrite_HOLE :: "'a::{}"
notation rewrite_HOLE ("HOLE")
notation rewrite_HOLE ("\<hole>")
lemma eta_expand:
fixes f :: "'a::{} \<Rightarrow> 'b::{}"
shows "f \<equiv> \<lambda>x. f x" .
lemma rewr_imp:
assumes "PROP A \<equiv> PROP B"
shows "(PROP A \<Longrightarrow> PROP C) \<equiv> (PROP B \<Longrightarrow> PROP C)"
apply (rule Pure.equal_intr_rule)
apply (drule equal_elim_rule2[OF assms]; assumption)
apply (drule equal_elim_rule1[OF assms]; assumption)
done
lemma imp_cong_eq:
"(PROP A \<Longrightarrow> (PROP B \<Longrightarrow> PROP C) \<equiv> (PROP B' \<Longrightarrow> PROP C')) \<equiv> ((PROP B \<Longrightarrow> PROP A \<Longrightarrow> PROP C) \<equiv> (PROP B' \<Longrightarrow> PROP A \<Longrightarrow> PROP C'))"
apply (intro Pure.equal_intr_rule)
apply (drule (1) cut_rl; drule Pure.equal_elim_rule1 Pure.equal_elim_rule2; assumption)+
apply (drule Pure.equal_elim_rule1 Pure.equal_elim_rule2; assumption)+
done
ML_file "cconv.ML"
ML_file "rewrite.ML"
end