1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/ftc/StrongIVT".
19 (* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *)
33 (*#* ** Strong IVT for partial functions
35 The IVT can be generalized to arbitrary partial functions; in the first
36 part, we will simply do that, repeating the previous construction.
38 The same notations and conventions apply as before.
41 inline cic:/CoRN/ftc/StrongIVT/a.var.
43 inline cic:/CoRN/ftc/StrongIVT/b.var.
45 inline cic:/CoRN/ftc/StrongIVT/Hab'.var.
47 inline cic:/CoRN/ftc/StrongIVT/Hab.var.
51 inline cic:/CoRN/ftc/StrongIVT/I.con.
53 inline cic:/CoRN/ftc/StrongIVT/I'.con.
57 inline cic:/CoRN/ftc/StrongIVT/F.var.
59 inline cic:/CoRN/ftc/StrongIVT/contF.var.
63 inline cic:/CoRN/ftc/StrongIVT/incF.con.
69 inline cic:/CoRN/ftc/StrongIVT/incrF.var.
75 inline cic:/CoRN/ftc/StrongIVT/Ha.con.
77 inline cic:/CoRN/ftc/StrongIVT/Hb.con.
79 inline cic:/CoRN/ftc/StrongIVT/HFab'.con.
85 inline cic:/CoRN/ftc/StrongIVT/z.var.
87 inline cic:/CoRN/ftc/StrongIVT/Haz.var.
89 inline cic:/CoRN/ftc/StrongIVT/Hzb.var.
93 inline cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con.
97 inline cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind.
99 inline cic:/CoRN/ftc/StrongIVT/IVT'_iter.con.
101 inline cic:/CoRN/ftc/StrongIVT/IVT'_seq.con.
103 inline cic:/CoRN/ftc/StrongIVT/a'_seq.con.
105 inline cic:/CoRN/ftc/StrongIVT/b'_seq.con.
107 inline cic:/CoRN/ftc/StrongIVT/a'_seq_I.con.
109 inline cic:/CoRN/ftc/StrongIVT/b'_seq_I.con.
111 inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con.
113 inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con.
115 inline cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con.
117 inline cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con.
119 inline cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con.
121 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con.
123 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con.
125 inline cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con.
127 inline cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con.
129 inline cic:/CoRN/ftc/StrongIVT/xa.con.
131 inline cic:/CoRN/ftc/StrongIVT/xb.con.
133 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con.
135 inline cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con.
137 inline cic:/CoRN/ftc/StrongIVT/IVT'_I.con.
143 (*#* **Other formulations
145 We now generalize the various statements of the intermediate value
146 theorem to more widely applicable forms.
149 inline cic:/CoRN/ftc/StrongIVT/Weak_IVT.con.
151 inline cic:/CoRN/ftc/StrongIVT/IVT_inc.con.
157 inline cic:/CoRN/ftc/StrongIVT/IVT_dec.con.
159 inline cic:/CoRN/ftc/StrongIVT/IVT'_inc.con.
165 inline cic:/CoRN/ftc/StrongIVT/IVT'_dec.con.