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theory Buffer_adm(* Title: HOLCF/FOCUS/Buffer_adm.thy ID: $Id: Buffer_adm.thy,v 1.4 2005/09/06 19:51:17 wenzelm Exp $ Author: David von Oheimb, TU Muenchen *) header {* One-element buffer, proof of Buf_Eq_imp_AC by induction + admissibility *} theory Buffer_adm imports Buffer Stream_adm begin end
theorem cont_BufAC_Asm_F:
down_cont BufAC_Asm_F
theorem BufAC_Asm_F_stream_monoP:
stream_monoP BufAC_Asm_F
theorem BufAC_Asm_F_stream_antiP:
stream_antiP BufAC_Asm_F
theorem adm_non_BufAC_Asm:
adm (%u. u ∉ BufAC_Asm)
theorem BufAC_Asm_cong:
[| f ∈ BufEq; ff ∈ BufEq; s ∈ BufAC_Asm |] ==> f·s = ff·s
theorem BufAC_Asm_antiton:
antitonP BufAC_Asm
theorem BufAC_Cmt_2stream_monoP:
f ∈ BufEq ==> ∃l. ∀i x s. s ∈ BufAC_Asm --> x << s --> Fin (l i) < #x --> (x, f·x) ∈ down_iterate BufAC_Cmt_F i --> (s, f·s) ∈ down_iterate BufAC_Cmt_F i
theorem BufAC_Cmt_iterate_all:
(x ∈ BufAC_Cmt) = (∀n. x ∈ down_iterate BufAC_Cmt_F n)
theorem adm_BufAC:
f ∈ BufEq ==> adm (%s. s ∈ BufAC_Asm --> (s, f·s) ∈ BufAC_Cmt)
theorem Buf_Eq_imp_AC:
BufEq ⊆ BufAC
theorem adm_BufAC_Asm:
adm (%x. x ∈ BufAC_Asm)
theorem adm_non_BufAC_Asm':
adm (%u. u ∉ BufAC_Asm)
theorem adm_BufAC':
f ∈ BufEq ==> adm (%u. u ∈ BufAC_Asm --> (u, f·u) ∈ BufAC_Cmt)