isabelle: src/FOL/ex/If.thy@e65314985426 (annotated)

41777 1f7cbe39d425 more precise headers; wenzelm parents: 35416 diff changeset	1	(* Title: FOL/ex/If.thy
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	2	Author: Lawrence C Paulson, Cambridge University Computer Laboratory
b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	3	Copyright 1991 University of Cambridge
14957 0e94a1ccc6ae tuned document; wenzelm parents: 14151 diff changeset	4	*)
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	5
60770 240563fbf41d isabelle update_cartouches; wenzelm parents: 58889 diff changeset	6	section \<open>First-Order Logic: the 'if' example\<close>
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	7
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	8	theory If
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	9	imports FOL
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	10	begin
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	11
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	12	definition "if" :: \<open>[o,o,o]=>o\<close>
e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	13	where \<open>if(P,Q,R) \<equiv> P \<and> Q \<or> \<not> P \<and> R\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	14
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	15	lemma ifI: \<open>\<lbrakk>P \<Longrightarrow> Q; \<not> P \<Longrightarrow> R\<rbrakk> \<Longrightarrow> if(P,Q,R)\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	16	unfolding if_def by blast
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	17
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	18	lemma ifE: \<open>\<lbrakk>if(P,Q,R); \<lbrakk>P; Q\<rbrakk> \<Longrightarrow> S; \<lbrakk>\<not> P; R\<rbrakk> \<Longrightarrow> S\<rbrakk> \<Longrightarrow> S\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	19	unfolding if_def by blast
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	20
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	21	lemma if_commute: \<open>if(P, if(Q,A,B), if(Q,C,D)) \<longleftrightarrow> if(Q, if(P,A,C), if(P,B,D))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	22	apply (rule iffI)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	23	apply (erule ifE)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	24	apply (erule ifE)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	25	apply (rule ifI)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	26	apply (rule ifI)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	27	oops
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	28
62020 5d208fd2507d isabelle update_cartouches -c -t; wenzelm parents: 61489 diff changeset	29	text\<open>Trying again from the beginning in order to use \<open>blast\<close>\<close>
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	30	declare ifI [intro!]
b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	31	declare ifE [elim!]
b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	32
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	33	lemma if_commute: \<open>if(P, if(Q,A,B), if(Q,C,D)) \<longleftrightarrow> if(Q, if(P,A,C), if(P,B,D))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	34	by blast
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	35
b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	36
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	37	lemma \<open>if(if(P,Q,R), A, B) \<longleftrightarrow> if(P, if(Q,A,B), if(R,A,B))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	38	by blast
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	39
60770 240563fbf41d isabelle update_cartouches; wenzelm parents: 58889 diff changeset	40	text\<open>Trying again from the beginning in order to prove from the definitions\<close>
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	41	lemma \<open>if(if(P,Q,R), A, B) \<longleftrightarrow> if(P, if(Q,A,B), if(R,A,B))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	42	unfolding if_def by blast
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	43
b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	44
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	45	text \<open>An invalid formula. High-level rules permit a simpler diagnosis.\<close>
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	46	lemma \<open>if(if(P,Q,R), A, B) \<longleftrightarrow> if(P, if(Q,A,B), if(R,B,A))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	47	apply auto
62020 5d208fd2507d isabelle update_cartouches -c -t; wenzelm parents: 61489 diff changeset	48	\<comment> \<open>The next step will fail unless subgoals remain\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	49	apply (tactic all_tac)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	50	oops
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	51
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	52	text \<open>Trying again from the beginning in order to prove from the definitions.\<close>
69590 e65314985426 isabelle update_inner_syntax_cartouches; wenzelm parents: 62020 diff changeset	53	lemma \<open>if(if(P,Q,R), A, B) \<longleftrightarrow> if(P, if(Q,A,B), if(R,B,A))\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	54	unfolding if_def
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	55	apply auto
62020 5d208fd2507d isabelle update_cartouches -c -t; wenzelm parents: 61489 diff changeset	56	\<comment> \<open>The next step will fail unless subgoals remain\<close>
61489 b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	57	apply (tactic all_tac)
b8d375aee0df more symbols; wenzelm parents: 60770 diff changeset	58	oops
14151 b8bb6a6a2c46 converting ex/If to Isar script paulson parents: 1322 diff changeset	59
0 a5a9c433f639 Initial revision clasohm parents: diff changeset	60	end

author	wenzelm
	Thu, 03 Jan 2019 22:19:19 +0100
changeset 69590	e65314985426
parent 62020	5d208fd2507d
permissions	-rw-r--r--