(*  Title:      HOL/Lifting_Sum.thy

    Author:     Brian Huffman and Ondrej Kuncar

*)

header {* Setup for Lifting/Transfer for the sum type *}

theory Lifting_Sum

imports Lifting Basic_BNFs

begin

(* The following lemma can be deleted when sum is added to FP sugar *)

lemma sum_pred_inject [simp]:

  "pred_sum P1 P2 (Inl a) = P1 a" and "pred_sum P1 P2 (Inr a) = P2 a"

  unfolding pred_sum_def fun_eq_iff sum_set_simps by auto

subsection {* Transfer rules for the Transfer package *}

context

begin

interpretation lifting_syntax .

lemma Inl_transfer [transfer_rule]: "(A ===> rel_sum A B) Inl Inl"

  unfolding rel_fun_def by simp

lemma Inr_transfer [transfer_rule]: "(B ===> rel_sum A B) Inr Inr"

  unfolding rel_fun_def by simp

lemma case_sum_transfer [transfer_rule]:

  "((A ===> C) ===> (B ===> C) ===> rel_sum A B ===> C) case_sum case_sum"

  unfolding rel_fun_def rel_sum_def by (simp split: sum.split)

end

end