src/HOL/Library/Rewrite.thy

consistent hosts ordering;

(*  Title:      HOL/Library/Rewrite.thy
    Author:     Christoph Traut, Lars Noschinski, TU Muenchen

Proof method "rewrite" with support for subterm-selection based on patterns.

Documentation: https://arxiv.org/abs/2111.04082
*)

theory Rewrite
imports Main
begin

consts rewrite_HOLE :: "'a::{}"  ("\<hole>")

lemma eta_expand:
  fixes f :: "'a::{} \<Rightarrow> 'b::{}"
  shows "f \<equiv> \<lambda>x. f x" .

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 \<open>cconv.ML\<close>
ML_file \<open>rewrite.ML\<close>

end