nominal2: Quot/QuotSum.thy@0b15b83ded4a (annotated)

934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	1	(* Title: QuotSum.thy
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	2	Author: Cezary Kaliszyk and Christian Urban
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	3	*)
698 ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	4	theory QuotSum
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	5	imports QuotMain
0 ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	6	begin
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	7
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	8	fun
545 95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	9	sum_rel
0 ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	10	where
545 95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	11	"sum_rel R1 R2 (Inl a1) (Inl b1) = R1 a1 b1"
95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	12	\| "sum_rel R1 R2 (Inl a1) (Inr b2) = False"
95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	13	\| "sum_rel R1 R2 (Inr a2) (Inl b1) = False"
95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	14	\| "sum_rel R1 R2 (Inr a2) (Inr b2) = R2 a2 b2"
0 ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	15
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	16	fun
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	17	sum_map
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	18	where
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	19	"sum_map f1 f2 (Inl a) = Inl (f1 a)"
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	20	\| "sum_map f1 f2 (Inr a) = Inr (f2 a)"
ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	21
779 3b21b24a5fb6 corrected map declarations for Sum and Prod; moved absrep_fun examples in separate file Christian Urban <urbanc@in.tum.de> parents: 698 diff changeset	22	declare [[map "+" = (sum_map, sum_rel)]]
3b21b24a5fb6 corrected map declarations for Sum and Prod; moved absrep_fun examples in separate file Christian Urban <urbanc@in.tum.de> parents: 698 diff changeset	23
545 95371a8b17e1 Cleaning the Quotients file Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 538 diff changeset	24
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	25	text {* should probably be in Sum_Type.thy *}
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	26	lemma split_sum_all:
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	27	shows "(\<forall>x. P x) \<longleftrightarrow> (\<forall>x. P (Inl x)) \<and> (\<forall>x. P (Inr x))"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	28	apply(auto)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	29	apply(case_tac x)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	30	apply(simp_all)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	31	done
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	32
698 ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	33	lemma sum_equivp[quot_equiv]:
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	34	assumes a: "equivp R1"
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	35	assumes b: "equivp R2"
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	36	shows "equivp (sum_rel R1 R2)"
924 5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	37	apply(rule equivpI)
5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	38	unfolding reflp_def symp_def transp_def
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	39	apply(simp_all add: split_sum_all)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	40	apply(blast intro: equivp_reflp[OF a] equivp_reflp[OF b])
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	41	apply(blast intro: equivp_symp[OF a] equivp_symp[OF b])
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	42	apply(blast intro: equivp_transp[OF a] equivp_transp[OF b])
924 5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	43	done
0 ebe0ea8fe247 initial commit Christian Urban <urbanc@in.tum.de> parents: diff changeset	44
698 ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	45	lemma sum_quotient[quot_thm]:
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	46	assumes q1: "Quotient R1 Abs1 Rep1"
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	47	assumes q2: "Quotient R2 Abs2 Rep2"
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	48	shows "Quotient (sum_rel R1 R2) (sum_map Abs1 Abs2) (sum_map Rep1 Rep2)"
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	49	unfolding Quotient_def
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	50	apply(simp add: split_sum_all)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	51	apply(simp_all add: Quotient_abs_rep[OF q1] Quotient_rel_rep[OF q1])
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	52	apply(simp_all add: Quotient_abs_rep[OF q2] Quotient_rel_rep[OF q2])
924 5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	53	using q1 q2
5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	54	unfolding Quotient_def
5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	55	apply(blast)+
698 ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	56	done
ed44eaaea63e Option and Sum quotients. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 613 diff changeset	57
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	58	lemma sum_Inl_rsp[quot_respect]:
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	59	assumes q1: "Quotient R1 Abs1 Rep1"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	60	assumes q2: "Quotient R2 Abs2 Rep2"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	61	shows "(R1 ===> sum_rel R1 R2) Inl Inl"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	62	by simp
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	63
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	64	lemma sum_Inr_rsp[quot_respect]:
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	65	assumes q1: "Quotient R1 Abs1 Rep1"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	66	assumes q2: "Quotient R2 Abs2 Rep2"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	67	shows "(R2 ===> sum_rel R1 R2) Inr Inr"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	68	by simp
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	69
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	70	lemma sum_Inl_prs[quot_respect]:
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	71	assumes q1: "Quotient R1 Abs1 Rep1"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	72	assumes q2: "Quotient R2 Abs2 Rep2"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	73	shows "(Rep1 ---> sum_map Abs1 Abs2) Inl = Inl"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	74	apply(simp add: expand_fun_eq)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	75	apply(simp add: Quotient_abs_rep[OF q1])
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	76	done
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	77
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	78	lemma sum_Inr_prs[quot_respect]:
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	79	assumes q1: "Quotient R1 Abs1 Rep1"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	80	assumes q2: "Quotient R2 Abs2 Rep2"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	81	shows "(Rep2 ---> sum_map Abs1 Abs2) Inr = Inr"
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	82	apply(simp add: expand_fun_eq)
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	83	apply(simp add: Quotient_abs_rep[OF q2])
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	84	done
0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	85
924 5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	86	lemma sum_map_id[id_simps]:
5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	87	shows "sum_map id id \<equiv> id"
829 42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	88	apply (rule eq_reflection)
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	89	apply (simp add: expand_fun_eq split_sum_all)
829 42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	90	done
42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	91
924 5455b19ef138 re-inserted lemma in QuotList Christian Urban <urbanc@in.tum.de> parents: 829 diff changeset	92	lemma sum_rel_eq[id_simps]:
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	93	shows "sum_rel (op =) (op =) \<equiv> (op =)"
829 42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	94	apply (rule eq_reflection)
934 0b15b83ded4a added prs and rsp lemmas for Inl and Inr Christian Urban <urbanc@in.tum.de> parents: 924 diff changeset	95	apply(simp add: expand_fun_eq split_sum_all)
829 42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	96	done
42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	97
42b90994ac77 map and rel simps for all quotients; needed when changing the relations to aggregate ones. Cezary Kaliszyk <kaliszyk@in.tum.de> parents: 779 diff changeset	98	end

author	Christian Urban <urbanc@in.tum.de>
	Tue, 26 Jan 2010 01:00:35 +0100
changeset 934	0b15b83ded4a
parent 924	5455b19ef138
child 936	da5e4b8317c7
permissions	-rw-r--r--