isabelle: src/HOLCF/Fix.thy@d2a06007ebfa (annotated)

2640 ee4dfce170a0 Changes of HOLCF from Oscar Slotosch: slotosch parents: 2275 diff changeset	1	(* Title: HOLCF/Fix.thy
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	2	ID: $Id$
1479 21eb5e156d91 expanded tabs clasohm parents: 1410 diff changeset	3	Author: Franz Regensburger
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	4	License: GPL (GNU GENERAL PUBLIC LICENSE)
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	5
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	6	definitions for fixed point operator and admissibility
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	7	*)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	8
15577 e16da3068ad6 fix headers huffman parents: 15576 diff changeset	9	header {* Fixed point operator and admissibility *}
e16da3068ad6 fix headers huffman parents: 15576 diff changeset	10
e16da3068ad6 fix headers huffman parents: 15576 diff changeset	11	theory Fix
e16da3068ad6 fix headers huffman parents: 15576 diff changeset	12	imports Cfun
e16da3068ad6 fix headers huffman parents: 15576 diff changeset	13	begin
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	14
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	15	consts
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	16
1990 9e23119c0219 added comment on is_flat oheimb parents: 1825 diff changeset	17	iterate :: "nat=>('a->'a)=>'a=>'a"
9e23119c0219 added comment on is_flat oheimb parents: 1825 diff changeset	18	Ifix :: "('a->'a)=>'a"
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	19	"fix" :: "('a->'a)->'a"
2841 c2508f4ab739 Added "discrete" CPOs and modified IMP to use those rather than "lift" nipkow parents: 2640 diff changeset	20	adm :: "('a::cpo=>bool)=>bool"
1990 9e23119c0219 added comment on is_flat oheimb parents: 1825 diff changeset	21	admw :: "('a=>bool)=>bool"
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	22
5192 704dd3a6d47d Adapted to new datatype package. berghofe parents: 4721 diff changeset	23	primrec
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	24	iterate_0: "iterate 0 F x = x"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	25	iterate_Suc: "iterate (Suc n) F x = F$(iterate n F x)"
5192 704dd3a6d47d Adapted to new datatype package. berghofe parents: 4721 diff changeset	26
1168 74be52691d62 The curried version of HOLCF is now just called HOLCF. The old regensbu parents: 1150 diff changeset	27	defs
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	28
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	29	Ifix_def: "Ifix F == lub(range(%i. iterate i F UU))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	30	fix_def: "fix == (LAM f. Ifix f)"
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	31
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	32	adm_def: "adm P == !Y. chain(Y) -->
3842 b55686a7b22c fixed dots; wenzelm parents: 3326 diff changeset	33	(!i. P(Y i)) --> P(lub(range Y))"
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	34
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	35	admw_def: "admw P == !F. (!n. P (iterate n F UU)) -->
1479 21eb5e156d91 expanded tabs clasohm parents: 1410 diff changeset	36	P (lub(range (%i. iterate i F UU)))"
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	37
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	38	text {* derive inductive properties of iterate from primitive recursion *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	39
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	40	lemma iterate_Suc2: "iterate (Suc n) F x = iterate n F (F$x)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	41	apply (induct_tac "n")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	42	apply auto
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	43	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	44
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	45	text {*
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	46	The sequence of function iterations is a chain.
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	47	This property is essential since monotonicity of iterate makes no sense.
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	48	*}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	49
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	50	lemma chain_iterate2: "x << F$x ==> chain (%i. iterate i F x)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	51	apply (rule chainI)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	52	apply (induct_tac "i")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	53	apply auto
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	54	apply (erule monofun_cfun_arg)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	55	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	56
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	57	lemma chain_iterate: "chain (%i. iterate i F UU)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	58	apply (rule chain_iterate2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	59	apply (rule minimal)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	60	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	61
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	62	text {*
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	63	Kleene's fixed point theorems for continuous functions in pointed
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	64	omega cpo's
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	65	*}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	66
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	67	lemma Ifix_eq: "Ifix F =F$(Ifix F)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	68	apply (unfold Ifix_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	69	apply (subst contlub_cfun_arg)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	70	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	71	apply (rule antisym_less)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	72	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	73	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	74	apply (rule ch2ch_Rep_CFunR)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	75	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	76	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	77	apply (rule iterate_Suc [THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	78	apply (rule chain_iterate [THEN chainE])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	79	apply (rule is_lub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	80	apply (rule ch2ch_Rep_CFunR)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	81	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	82	apply (rule ub_rangeI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	83	apply (rule iterate_Suc [THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	84	apply (rule is_ub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	85	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	86	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	87
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	88	lemma Ifix_least: "F$x=x ==> Ifix(F) << x"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	89	apply (unfold Ifix_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	90	apply (rule is_lub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	91	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	92	apply (rule ub_rangeI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	93	apply (induct_tac "i")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	94	apply (simp (no_asm_simp))
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	95	apply (simp (no_asm_simp))
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	96	apply (rule_tac t = "x" in subst)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	97	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	98	apply (erule monofun_cfun_arg)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	99	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	100
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	101	text {* monotonicity and continuity of @{term iterate} *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	102
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	103	lemma monofun_iterate: "monofun(iterate(i))"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	104	apply (rule monofunI [rule_format])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	105	apply (induct_tac "i")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	106	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	107	apply (simp add: less_fun monofun_cfun)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	108	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	109
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	110	text {*
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	111	The following lemma uses @{thm [source] contlub_cfun} which itself is based
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	112	on a diagonalisation lemma for continuous functions with two arguments. In
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	113	this special case it is the application function @{term Rep_CFun}
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	114	*}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	115
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	116	lemma contlub_iterate: "contlub(iterate(i))"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	117	apply (rule contlubI [rule_format])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	118	apply (induct_tac "i")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	119	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	120	apply (rule lub_const [THEN thelubI, symmetric])
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	121	apply (simp del: range_composition)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	122	apply (rule ext)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	123	apply (simplesubst thelub_fun)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	124	apply (rule chainI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	125	apply (rule less_fun [THEN iffD2])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	126	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	127	apply (rule chainE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	128	apply (rule monofun_Rep_CFun1 [THEN ch2ch_MF2LR])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	129	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	130	apply (rule monofun_Rep_CFun2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	131	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	132	apply (rule ch2ch_fun)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	133	apply (rule monofun_iterate [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	134	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	135	apply (subst thelub_fun)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	136	apply (rule monofun_iterate [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	137	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	138	apply (rule contlub_cfun)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	139	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	140	apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	141	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	142
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	143	lemma cont_iterate: "cont(iterate(i))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	144	apply (rule monocontlub2cont)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	145	apply (rule monofun_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	146	apply (rule contlub_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	147	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	148
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	149	text {* a lemma about continuity of @{term iterate} in its third argument *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	150
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	151	lemma monofun_iterate2: "monofun(iterate n F)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	152	apply (rule monofunI [rule_format])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	153	apply (induct_tac "n")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	154	apply (simp)
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	155	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	156	apply (erule monofun_cfun_arg)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	157	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	158
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	159	lemma contlub_iterate2: "contlub(iterate n F)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	160	apply (rule contlubI [rule_format])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	161	apply (induct_tac "n")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	162	apply (simp)
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	163	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	164	apply (rule_tac t = "iterate n F (lub (range (%u. Y u))) " and s = "lub (range (%i. iterate n F (Y i))) " in ssubst)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	165	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	166	apply (rule contlub_cfun_arg)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	167	apply (erule monofun_iterate2 [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	168	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	169
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	170	lemma cont_iterate2: "cont (iterate n F)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	171	apply (rule monocontlub2cont)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	172	apply (rule monofun_iterate2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	173	apply (rule contlub_iterate2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	174	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	175
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	176	text {* monotonicity and continuity of @{term Ifix} *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	177
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	178	lemma monofun_Ifix: "monofun(Ifix)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	179	apply (rule monofunI [rule_format])
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	180	apply (unfold Ifix_def)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	181	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	182	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	183	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	184	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	185	apply (rule less_fun [THEN iffD1, THEN spec], erule monofun_iterate [THEN monofunE, THEN spec, THEN spec, THEN mp])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	186	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	187
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	188	text {*
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	189	since iterate is not monotone in its first argument, special lemmas must
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	190	be derived for lubs in this argument
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	191	*}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	192
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	193	lemma chain_iterate_lub:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	194	"chain(Y) ==> chain(%i. lub(range(%ia. iterate ia (Y i) UU)))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	195	apply (rule chainI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	196	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	197	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	198	apply (rule chain_iterate)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	199	apply (rule allI)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	200	apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun, THEN chainE])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	201	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	202
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	203	text {*
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	204	this exchange lemma is analog to the one for monotone functions
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	205	observe that monotonicity is not really needed. The propagation of
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	206	chains is the essential argument which is usually derived from monot.
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	207	*}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	208
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	209	lemma contlub_Ifix_lemma1: "chain(Y) ==>iterate n (lub(range Y)) y = lub(range(%i. iterate n (Y i) y))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	210	apply (rule thelub_fun [THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	211	apply (erule monofun_iterate [THEN ch2ch_monofun])
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	212	apply (simp add: contlub_iterate [THEN contlubE])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	213	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	214
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	215	lemma ex_lub_iterate: "chain(Y) ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	216	lub(range(%i. lub(range(%ia. iterate i (Y ia) UU)))) =
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	217	lub(range(%i. lub(range(%ia. iterate ia (Y i) UU))))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	218	apply (rule antisym_less)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	219	apply (rule is_lub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	220	apply (rule contlub_Ifix_lemma1 [THEN ext, THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	221	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	222	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	223	apply (rule ub_rangeI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	224	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	225	apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	226	apply (erule chain_iterate_lub)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	227	apply (rule allI)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	228	apply (rule is_ub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	229	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	230	apply (rule is_lub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	231	apply (erule chain_iterate_lub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	232	apply (rule ub_rangeI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	233	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	234	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	235	apply (rule contlub_Ifix_lemma1 [THEN ext, THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	236	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	237	apply (rule chain_iterate)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	238	apply (rule allI)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	239	apply (rule is_ub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	240	apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	241	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	242
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	243	lemma contlub_Ifix: "contlub(Ifix)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	244	apply (rule contlubI [rule_format])
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	245	apply (unfold Ifix_def)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	246	apply (subst contlub_Ifix_lemma1 [THEN ext])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	247	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	248	apply (erule ex_lub_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	249	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	250
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	251	lemma cont_Ifix: "cont(Ifix)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	252	apply (rule monocontlub2cont)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	253	apply (rule monofun_Ifix)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	254	apply (rule contlub_Ifix)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	255	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	256
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	257	text {* propagate properties of @{term Ifix} to its continuous counterpart *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	258
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	259	lemma fix_eq: "fix$F = F$(fix$F)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	260	apply (unfold fix_def)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	261	apply (simp add: cont_Ifix)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	262	apply (rule Ifix_eq)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	263	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	264
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	265	lemma fix_least: "F$x = x ==> fix$F << x"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	266	apply (unfold fix_def)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	267	apply (simp add: cont_Ifix)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	268	apply (erule Ifix_least)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	269	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	270
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	271	lemma fix_eqI:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	272	"[\| F$x = x; !z. F$z = z --> x << z \|] ==> x = fix$F"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	273	apply (rule antisym_less)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	274	apply (erule allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	275	apply (erule mp)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	276	apply (rule fix_eq [symmetric])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	277	apply (erule fix_least)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	278	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	279
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	280	lemma fix_eq2: "f == fix$F ==> f = F$f"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	281	by (simp add: fix_eq [symmetric])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	282
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	283	lemma fix_eq3: "f == fix$F ==> f$x = F$f$x"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	284	by (erule fix_eq2 [THEN cfun_fun_cong])
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	285
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	286	(* fun fix_tac3 thm i = ((rtac trans i) THEN (rtac (thm RS fix_eq3) i)) *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	287
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	288	lemma fix_eq4: "f = fix$F ==> f = F$f"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	289	apply (erule ssubst)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	290	apply (rule fix_eq)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	291	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	292
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	293	lemma fix_eq5: "f = fix$F ==> f$x = F$f$x"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	294	apply (rule trans)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	295	apply (erule fix_eq4 [THEN cfun_fun_cong])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	296	apply (rule refl)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	297	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	298
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	299	(* fun fix_tac5 thm i = ((rtac trans i) THEN (rtac (thm RS fix_eq5) i)) *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	300
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	301	(* proves the unfolding theorem for function equations f = fix$... *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	302	(*
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	303	fun fix_prover thy fixeq s = prove_goal thy s (fn prems => [
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	304	(rtac trans 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	305	(rtac (fixeq RS fix_eq4) 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	306	(rtac trans 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	307	(rtac beta_cfun 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	308	(Simp_tac 1)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	309	])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	310	*)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	311	(* proves the unfolding theorem for function definitions f == fix$... *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	312	(*
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	313	fun fix_prover2 thy fixdef s = prove_goal thy s (fn prems => [
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	314	(rtac trans 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	315	(rtac (fix_eq2) 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	316	(rtac fixdef 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	317	(rtac beta_cfun 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	318	(Simp_tac 1)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	319	])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	320	*)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	321	(* proves an application case for a function from its unfolding thm *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	322	(*
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	323	fun case_prover thy unfold s = prove_goal thy s (fn prems => [
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	324	(cut_facts_tac prems 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	325	(rtac trans 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	326	(stac unfold 1),
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	327	Auto_tac
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	328	])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	329	*)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	330	text {* better access to definitions *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	331
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	332	lemma Ifix_def2: "Ifix=(%x. lub(range(%i. iterate i x UU)))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	333	apply (rule ext)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	334	apply (unfold Ifix_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	335	apply (rule refl)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	336	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	337
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	338	text {* direct connection between @{term fix} and iteration without @{term Ifix} *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	339
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	340	lemma fix_def2: "fix$F = lub(range(%i. iterate i F UU))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	341	apply (unfold fix_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	342	apply (fold Ifix_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	343	apply (simp (no_asm_simp) add: cont_Ifix)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	344	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	345
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	346	text {* Lemmas about admissibility and fixed point induction *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	347
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	348	text {* access to definitions *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	349
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	350	lemma admI:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	351	"(!!Y. [\| chain Y; !i. P (Y i) \|] ==> P (lub (range Y))) ==> adm P"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	352	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	353	apply blast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	354	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	355
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	356	lemma triv_admI: "!x. P x ==> adm P"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	357	apply (rule admI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	358	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	359	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	360
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	361	lemma admD: "[\| adm(P); chain(Y); !i. P(Y(i)) \|] ==> P(lub(range(Y)))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	362	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	363	apply blast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	364	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	365
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	366	lemma admw_def2: "admw(P) = (!F.(!n. P(iterate n F UU)) -->
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	367	P (lub(range(%i. iterate i F UU))))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	368	apply (unfold admw_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	369	apply (rule refl)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	370	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	371
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	372	text {* an admissible formula is also weak admissible *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	373
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	374	lemma adm_impl_admw: "adm(P)==>admw(P)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	375	apply (unfold admw_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	376	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	377	apply (erule admD)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	378	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	379	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	380	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	381
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	382	text {* fixed point induction *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	383
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	384	lemma fix_ind:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	385	"[\| adm(P); P(UU); !!x. P(x) ==> P(F$x)\|] ==> P(fix$F)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	386	apply (subst fix_def2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	387	apply (erule admD)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	388	apply (rule chain_iterate)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	389	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	390	apply (induct_tac "i")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	391	apply simp
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	392	apply simp
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	393	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	394
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	395	lemma def_fix_ind: "[\| f == fix$F; adm(P);
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	396	P(UU); !!x. P(x) ==> P(F$x)\|] ==> P f"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	397	apply simp
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	398	apply (erule fix_ind)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	399	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	400	apply fast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	401	done
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	402
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	403	text {* computational induction for weak admissible formulae *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	404
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	405	lemma wfix_ind: "[\| admw(P); !n. P(iterate n F UU)\|] ==> P(fix$F)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	406	apply (subst fix_def2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	407	apply (rule admw_def2 [THEN iffD1, THEN spec, THEN mp])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	408	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	409	apply (rule allI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	410	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	411	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	412
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	413	lemma def_wfix_ind: "[\| f == fix$F; admw(P);
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	414	!n. P(iterate n F UU) \|] ==> P f"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	415	apply simp
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	416	apply (erule wfix_ind)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	417	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	418	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	419
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	420	text {* for chain-finite (easy) types every formula is admissible *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	421
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	422	lemma adm_max_in_chain:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	423	"!Y. chain(Y::nat=>'a) --> (? n. max_in_chain n Y) ==> adm(P::'a=>bool)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	424	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	425	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	426	apply (rule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	427	apply (rule mp)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	428	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	429	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	430	apply (subst lub_finch1 [THEN thelubI])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	431	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	432	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	433	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	434	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	435
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	436	lemmas adm_chfin = chfin [THEN adm_max_in_chain, standard]
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	437
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	438	text {* some lemmata for functions with flat/chfin domain/range types *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	439
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	440	lemma adm_chfindom: "adm (%(u::'a::cpo->'b::chfin). P(u$s))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	441	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	442	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	443	apply (drule chfin_Rep_CFunR)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	444	apply (erule_tac x = "s" in allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	445	apply clarsimp
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	446	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	447
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	448	(* adm_flat not needed any more, since it is a special case of adm_chfindom *)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	449
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	450	text {* improved admissibility introduction *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	451
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	452	lemma admI2:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	453	"(!!Y. [\| chain Y; !i. P (Y i); !i. ? j. i < j & Y i ~= Y j & Y i << Y j \|]
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	454	==> P(lub (range Y))) ==> adm P"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	455	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	456	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	457	apply (erule increasing_chain_adm_lemma)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	458	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	459	apply fast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	460	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	461
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	462	text {* admissibility of special formulae and propagation *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	463
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	464	lemma adm_less [simp]: "[\|cont u;cont v\|]==> adm(%x. u x << v x)"
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	465	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	466	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	467	apply (frule_tac f = "u" in cont2mono [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	468	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	469	apply (frule_tac f = "v" in cont2mono [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	470	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	471	apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN ssubst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	472	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	473	apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN ssubst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	474	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	475	apply (blast intro: lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	476	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	477
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	478	lemma adm_conj [simp]: "[\| adm P; adm Q \|] ==> adm(%x. P x & Q x)"
d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	479	by (fast elim: admD intro: admI)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	480
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	481	lemma adm_not_free [simp]: "adm(%x. t)"
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	482	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	483	apply fast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	484	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	485
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	486	lemma adm_not_less: "cont t ==> adm(%x.~ (t x) << u)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	487	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	488	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	489	apply (rule contrapos_nn)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	490	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	491	apply (rule trans_less)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	492	prefer 2 apply (assumption)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	493	apply (erule cont2mono [THEN monofun_fun_arg])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	494	apply (rule is_ub_thelub)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	495	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	496	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	497
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	498	lemma adm_all: "!y. adm(P y) ==> adm(%x.!y. P y x)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	499	by (fast intro: admI elim: admD)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	500
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	501	lemmas adm_all2 = allI [THEN adm_all, standard]
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	502
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	503	lemma adm_subst: "[\|cont t; adm P\|] ==> adm(%x. P (t x))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	504	apply (rule admI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	505	apply (simplesubst cont2contlub [THEN contlubE, THEN spec, THEN mp])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	506	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	507	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	508	apply (erule admD)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	509	apply (erule cont2mono [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	510	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	511	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	512	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	513
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	514	lemma adm_UU_not_less: "adm(%x.~ UU << t(x))"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	515	by simp
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	516
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	517	lemma adm_not_UU: "cont(t)==> adm(%x.~ (t x) = UU)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	518	apply (unfold adm_def)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	519	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	520	apply (rule contrapos_nn)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	521	apply (erule spec)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	522	apply (rule chain_UU_I [THEN spec])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	523	apply (erule cont2mono [THEN ch2ch_monofun])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	524	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	525	apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN subst])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	526	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	527	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	528	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	529
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	530	lemma adm_eq: "[\|cont u ; cont v\|]==> adm(%x. u x = v x)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	531	by (simp add: po_eq_conv)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	532
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	533	text {* admissibility for disjunction is hard to prove. It takes 10 Lemmas *}
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	534
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	535	lemma adm_disj_lemma1: "!n. P(Y n)\|Q(Y n) ==> (? i.!j. R i j --> Q(Y(j))) \| (!i.? j. R i j & P(Y(j)))"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	536	by fast
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	537
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	538	lemma adm_disj_lemma2: "[\| adm(Q); ? X. chain(X) & (!n. Q(X(n))) &
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	539	lub(range(Y))=lub(range(X))\|] ==> Q(lub(range(Y)))"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	540	by (force elim: admD)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	541
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	542	lemma adm_disj_lemma3: "chain Y ==> chain (%m. if m < Suc i then Y (Suc i) else Y m)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	543	apply (unfold chain_def)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	544	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	545	apply safe
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	546	apply (subgoal_tac "ia = i")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	547	apply (simp_all)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	548	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	549
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	550	lemma adm_disj_lemma4: "!j. i < j --> Q(Y(j)) ==> !n. Q( if n < Suc i then Y(Suc i) else Y n)"
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	551	by (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	552
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	553	lemma adm_disj_lemma5:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	554	"!!Y::nat=>'a::cpo. [\| chain(Y); ! j. i < j --> Q(Y(j)) \|] ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	555	lub(range(Y)) = lub(range(%m. if m< Suc(i) then Y(Suc(i)) else Y m))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	556	apply (safe intro!: lub_equal2 adm_disj_lemma3)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	557	prefer 2 apply (assumption)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	558	apply (rule_tac x = "i" in exI)
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	559	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	560	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	561
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	562	lemma adm_disj_lemma6:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	563	"[\| chain(Y::nat=>'a::cpo); ? i. ! j. i < j --> Q(Y(j)) \|] ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	564	? X. chain(X) & (! n. Q(X(n))) & lub(range(Y)) = lub(range(X))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	565	apply (erule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	566	apply (rule_tac x = "%m. if m<Suc (i) then Y (Suc (i)) else Y m" in exI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	567	apply (rule conjI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	568	apply (rule adm_disj_lemma3)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	569	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	570	apply (rule conjI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	571	apply (rule adm_disj_lemma4)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	572	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	573	apply (rule adm_disj_lemma5)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	574	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	575	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	576	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	577
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	578	lemma adm_disj_lemma7:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	579	"[\| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) \|] ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	580	chain(%m. Y(Least(%j. m<j & P(Y(j)))))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	581	apply (rule chainI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	582	apply (rule chain_mono3)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	583	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	584	apply (rule Least_le)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	585	apply (rule conjI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	586	apply (rule Suc_lessD)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	587	apply (erule allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	588	apply (erule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	589	apply (rule LeastI [THEN conjunct1])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	590	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	591	apply (erule allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	592	apply (erule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	593	apply (rule LeastI [THEN conjunct2])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	594	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	595	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	596
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	597	lemma adm_disj_lemma8:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	598	"[\| ! i. ? j. i < j & P(Y(j)) \|] ==> ! m. P(Y(LEAST j::nat. m<j & P(Y(j))))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	599	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	600	apply (erule allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	601	apply (erule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	602	apply (erule LeastI [THEN conjunct2])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	603	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	604
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	605	lemma adm_disj_lemma9:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	606	"[\| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) \|] ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	607	lub(range(Y)) = lub(range(%m. Y(Least(%j. m<j & P(Y(j))))))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	608	apply (rule antisym_less)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	609	apply (rule lub_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	610	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	611	apply (rule adm_disj_lemma7)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	612	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	613	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	614	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	615	apply (rule chain_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	616	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	617	apply (erule allE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	618	apply (erule exE)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	619	apply (rule LeastI [THEN conjunct1])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	620	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	621	apply (rule lub_mono3)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	622	apply (rule adm_disj_lemma7)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	623	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	624	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	625	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	626	apply (intro strip)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	627	apply (rule exI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	628	apply (rule chain_mono)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	629	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	630	apply (rule lessI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	631	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	632
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	633	lemma adm_disj_lemma10: "[\| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) \|] ==>
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	634	? X. chain(X) & (! n. P(X(n))) & lub(range(Y)) = lub(range(X))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	635	apply (rule_tac x = "%m. Y (Least (%j. m<j & P (Y (j))))" in exI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	636	apply (rule conjI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	637	apply (rule adm_disj_lemma7)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	638	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	639	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	640	apply (rule conjI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	641	apply (rule adm_disj_lemma8)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	642	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	643	apply (rule adm_disj_lemma9)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	644	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	645	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	646	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	647
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	648	lemma adm_disj_lemma12: "[\| adm(P); chain(Y);? i. ! j. i < j --> P(Y(j))\|]==>P(lub(range(Y)))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	649	apply (erule adm_disj_lemma2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	650	apply (erule adm_disj_lemma6)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	651	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	652	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	653
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	654	lemma adm_lemma11:
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	655	"[\| adm(P); chain(Y); ! i. ? j. i < j & P(Y(j)) \|]==>P(lub(range(Y)))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	656	apply (erule adm_disj_lemma2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	657	apply (erule adm_disj_lemma10)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	658	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	659	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	660
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	661	lemma adm_disj: "[\| adm P; adm Q \|] ==> adm(%x. P x \| Q x)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	662	apply (rule admI)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	663	apply (rule adm_disj_lemma1 [THEN disjE])
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	664	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	665	apply (rule disjI2)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	666	apply (erule adm_disj_lemma12)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	667	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	668	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	669	apply (rule disjI1)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	670	apply (erule adm_lemma11)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	671	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	672	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	673	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	674
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	675	lemma adm_imp: "[\| adm(%x.~(P x)); adm Q \|] ==> adm(%x. P x --> Q x)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	676	apply (subgoal_tac " (%x. P x --> Q x) = (%x. ~P x \| Q x) ")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	677	apply (erule ssubst)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	678	apply (erule adm_disj)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	679	apply assumption
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	680	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	681	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	682
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	683	lemma adm_iff: "[\| adm (%x. P x --> Q x); adm (%x. Q x --> P x) \|]
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	684	==> adm (%x. P x = Q x)"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	685	apply (subgoal_tac " (%x. P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))")
15637 d2a06007ebfa changed comments to text blocks, cleaned up a few proofs huffman parents: 15577 diff changeset	686	apply (simp)
15576 efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	687	apply (rule ext)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	688	apply fast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	689	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	690
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	691
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	692	lemma adm_not_conj: "[\| adm (%x. ~ P x); adm (%x. ~ Q x) \|] ==> adm (%x. ~ (P x & Q x))"
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	693	apply (subgoal_tac " (%x. ~ (P x & Q x)) = (%x. ~ P x \| ~ Q x) ")
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	694	apply (rule_tac [2] ext)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	695	prefer 2 apply fast
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	696	apply (erule ssubst)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	697	apply (erule adm_disj)
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	698	apply assumption
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	699	done
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	700
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	701	lemmas adm_lemmas = adm_not_free adm_imp adm_disj adm_eq adm_not_UU
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	702	adm_UU_not_less adm_all2 adm_not_less adm_not_conj adm_iff
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	703
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	704	declare adm_lemmas [simp]
efb95d0d01f7 converted to new-style theories, and combined numbered files huffman parents: 14981 diff changeset	705
243 c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	706	end
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF nipkow parents: diff changeset	707

author	huffman
	Thu, 31 Mar 2005 00:10:35 +0200
changeset 15637	d2a06007ebfa
parent 15577	e16da3068ad6
child 15857	83cb9dae3817
permissions	-rw-r--r--