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[helm.git] / matita / contribs / CoRN-Decl / devel / loeb / IDA / Ch6.ma

diff --git a/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma b/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma
new file mode 100644 (file)
index 0000000..fe7031a
--- /dev/null
+++ b/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma
@@ -0,0 +1,627 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/IDA/Ch6".
+
+include "CoRN.ma".
+
+include "algebra/CSemiGroups.ma".
+
+(* Remark blz 65 1 *)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con".
+
+include "model/setoids/Zsetoid.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con".
+
+(* Remark blz 65 2 *)
+
+include "devel/loeb/per/csetfun.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con".
+
+include "model/setoids/Nsetoid.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/on.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__".
+
+(* blz 65 Example 1 *)
+
+(* Print Zopp_is_fun.*)
+
+(* Print Inv_as_un_op.
+Geen goed voorbeeld: monoids komen hier al in voor en het is een heel onoverzichtelijk bewijs *)
+
+(* blz 65 Example 2 *)
+
+(* Print plus_is_bin_fun.*)
+
+(* Print mult_as_bin_fun.*)
+
+(* blz 66 Example 1 *)
+
+(* Print plus_is_assoc.*)
+
+(* Print Zplus_is_assoc.*)
+
+(* Print Zmult_is_assoc.*)
+
+include "model/setoids/Qsetoid.ma".
+
+(* Print Qplus_is_assoc.*)
+
+(* Print Qmult_is_assoc.*)
+
+(* blz 66 Examples 2 *)
+
+(* UNEXPORTED
+Section p66E2
+*)
+
+alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var".
+
+alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var".
+
+alias id "g" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var".
+
+alias id "h" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var".
+
+(* Check comp_as_bin_op.*)
+
+(* Check assoc_comp.*)
+
+(* UNEXPORTED
+End p66E2
+*)
+
+(* blz 66 Example 2eblok 1 *)
+
+include "model/semigroups/Zsemigroup.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con".
+
+(* blz 66 Example % 3 *)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con".
+
+(* blz 66 Example % 4 *)
+
+(* UNEXPORTED
+Section p66E2b4
+*)
+
+alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con".
+
+include "algebra/CSemiGroups.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con".
+
+(* UNEXPORTED
+End p66E2b4
+*)
+
+(* Definition 5 *)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con".
+
+(* blz 67 Remark 1 *)
+
+include "model/monoids/Zmonoid.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con".
+
+(* blz 67 Remark 2 *)
+
+(* UNEXPORTED
+Section p67R2
+*)
+
+alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con".
+
+(* UNEXPORTED
+End p67R2
+*)
+
+(* blz 67 Remark 3 *)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con".
+
+(* Lemma 6 *)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con".
+
+(* blz 67 Example 1 *)
+
+include "model/monoids/Nmonoid.ma".
+
+(* Print nat_is_CMonoid.*)
+
+include "model/monoids/Zmonoid.ma".
+
+(* Print Z_is_CMonoid.*)
+
+(* Print Z_mul_is_CMonoid.*)
+
+(* blz 67 Example 3 *)
+
+(* Print FS_is_CMonoid.*)
+
+(* blz 68 Example blok1 1 *)
+
+(* UNEXPORTED
+Section p68E1b1
+*)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con".
+
+include "algebra/CMonoids.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con".
+
+(* UNEXPORTED
+End p68E1b1
+*)
+
+(* blz 68 Example blok2 1 *)
+
+(* Print Zplus_is_commut.*)
+
+(* Print Zmult_is_commut. *)
+
+(* Print Qplus_is_commut1. *)
+
+(* Print Qmult_is_commut. *)
+
+(* Definition 9 *)
+
+include "algebra/CMonoids.ma".
+
+(* UNEXPORTED
+Section D9S
+*)
+
+alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var".
+
+alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con".
+
+(* UNEXPORTED
+End D9S
+*)
+
+(* UNEXPORTED
+Section D9M
+*)
+
+alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var".
+
+alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con".
+
+(* UNEXPORTED
+End D9M
+*)
+
+(* blz 69 Example *)
+
+(* UNEXPORTED
+Section p69E1
+*)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con".
+
+(* UNEXPORTED
+End p69E1
+*)
+
+(* Theorem 11 *)
+
+(* UNEXPORTED
+Section Th11
+*)
+
+alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var".
+
+alias id "I" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var".
+
+alias id "C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var".
+
+alias id "Cunit" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var".
+
+alias id "op_pres_C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/K.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con".
+
+(* UNEXPORTED
+End Th11
+*)
+
+(* Theorem 12 *)
+
+(* UNEXPORTED
+Section Th12
+*)
+
+alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con".
+
+(* UNEXPORTED
+End Th12
+*)
+
+(* blz 70 text *)
+
+(* UNEXPORTED
+Section p70text
+*)
+
+include "devel/loeb/per/lst2fun.ma".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con".
+
+(* UNEXPORTED
+End p70text
+*)
+
+(* Definition 13 *)
+
+(* UNEXPORTED
+Section Th13
+*)
+
+alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var".
+
+alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con".
+
+(* UNEXPORTED
+End Th13
+*)
+
+(* blz 71 Example 1 *)
+
+(* UNEXPORTED
+Section p71E1
+*)
+
+alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var".
+
+alias id "c" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con".
+
+alias id "is_generated_by" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con".
+
+(* UNEXPORTED
+End p71E1
+*)
+
+(* UNEXPORTED
+Section p71E1'
+*)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con".
+
+(* UNEXPORTED
+End p71E1'
+*)
+
+(* Print to_word_bijective.*)
+
+(* UNEXPORTED
+Section p71E2
+*)
+
+alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con".
+
+(* UNEXPORTED
+End p71E2
+*)
+
+(* blz 71 Remark 1 *)
+
+(* UNEXPORTED
+Section p71R1
+*)
+
+alias id "S1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var".
+
+alias id "S2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con".
+
+(* UNEXPORTED
+End p71R1
+*)
+
+(* UNEXPORTED
+Section p71R2
+*)
+
+alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con".
+
+(* UNEXPORTED
+End p71R2
+*)
+
+(* Theorem 14 *)
+
+(* UNEXPORTED
+Section Th14
+*)
+
+alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var".
+
+alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var".
+
+alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var".
+
+alias id "isof" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con".
+
+(* UNEXPORTED
+End Th14
+*)
+
+(* blz 71 Examples 2eblok 1 *)
+
+(* UNEXPORTED
+Section p71E2b1
+*)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con".
+
+(* UNEXPORTED
+End p71E2b1
+*)
+
+(* UNEXPORTED
+Section p71E2b2
+*)
+
+alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var".
+
+alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con".
+
+(* UNEXPORTED
+End p71E2b2
+*)
+
+(* UNEXPORTED
+Section Th15
+*)
+
+alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con".
+
+alias id "D" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/member.con".
+
+(* UNEXPORTED
+Implicit Arguments member [A].
+*)
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con".
+
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con".
+
+(* UNEXPORTED
+End Th15
+*)
+