X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fcomplex%2FCComplex.ma;h=6cf6aa340d243b270212274e1666c19a6779cf05;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=084598506096e4a483595a5b5810c5bcf7f08f99;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma b/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma index 084598506..6cf6aa340 100644 --- a/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma +++ b/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex". +include "CoRN.ma". + (* $Id: CComplex.v,v 1.8 2004/04/23 10:00:55 lcf Exp $ *) (*#* printing Re %\ensuremath{\Re}% #ℜ# *) @@ -32,9 +34,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex". (*#* printing CCX %\ensuremath{\mathbb C[X]}% #C[X]# *) -(* INCLUDE -NRootIR -*) +include "reals/NRootIR.ma". (*#* * Complex Numbers ** Algebraic structure @@ -44,27 +44,27 @@ NRootIR Section Complex_Numbers. *) -inline cic:/CoRN/complex/CComplex/CC_set.ind. +inline "cic:/CoRN/complex/CComplex/CC_set.ind". -inline cic:/CoRN/complex/CComplex/cc_ap.con. +inline "cic:/CoRN/complex/CComplex/cc_ap.con". -inline cic:/CoRN/complex/CComplex/cc_eq.con. +inline "cic:/CoRN/complex/CComplex/cc_eq.con". -inline cic:/CoRN/complex/CComplex/cc_is_CSetoid.con. +inline "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con". -inline cic:/CoRN/complex/CComplex/cc_csetoid.con. +inline "cic:/CoRN/complex/CComplex/cc_csetoid.con". -inline cic:/CoRN/complex/CComplex/cc_plus.con. +inline "cic:/CoRN/complex/CComplex/cc_plus.con". -inline cic:/CoRN/complex/CComplex/cc_mult.con. +inline "cic:/CoRN/complex/CComplex/cc_mult.con". -inline cic:/CoRN/complex/CComplex/cc_zero.con. +inline "cic:/CoRN/complex/CComplex/cc_zero.con". -inline cic:/CoRN/complex/CComplex/cc_one.con. +inline "cic:/CoRN/complex/CComplex/cc_one.con". -inline cic:/CoRN/complex/CComplex/cc_i.con. +inline "cic:/CoRN/complex/CComplex/cc_i.con". -inline cic:/CoRN/complex/CComplex/cc_inv.con. +inline "cic:/CoRN/complex/CComplex/cc_inv.con". (* not needed anymore Lemma cc_plus_op_proof : (bin_op_wd cc_csetoid cc_plus). @@ -92,56 +92,56 @@ Split; Algebra. Qed. *) -inline cic:/CoRN/complex/CComplex/cc_inv_strext.con. +inline "cic:/CoRN/complex/CComplex/cc_inv_strext.con". -inline cic:/CoRN/complex/CComplex/cc_plus_strext.con. +inline "cic:/CoRN/complex/CComplex/cc_plus_strext.con". -inline cic:/CoRN/complex/CComplex/cc_mult_strext.con. +inline "cic:/CoRN/complex/CComplex/cc_mult_strext.con". -inline cic:/CoRN/complex/CComplex/cc_inv_op.con. +inline "cic:/CoRN/complex/CComplex/cc_inv_op.con". -inline cic:/CoRN/complex/CComplex/cc_plus_op.con. +inline "cic:/CoRN/complex/CComplex/cc_plus_op.con". -inline cic:/CoRN/complex/CComplex/cc_mult_op.con. +inline "cic:/CoRN/complex/CComplex/cc_mult_op.con". -inline cic:/CoRN/complex/CComplex/cc_csg_associative.con. +inline "cic:/CoRN/complex/CComplex/cc_csg_associative.con". -inline cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con. +inline "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con". -inline cic:/CoRN/complex/CComplex/cc_csemi_grp.con. +inline "cic:/CoRN/complex/CComplex/cc_csemi_grp.con". -inline cic:/CoRN/complex/CComplex/cc_cm_proof.con. +inline "cic:/CoRN/complex/CComplex/cc_cm_proof.con". -inline cic:/CoRN/complex/CComplex/cc_cmonoid.con. +inline "cic:/CoRN/complex/CComplex/cc_cmonoid.con". -inline cic:/CoRN/complex/CComplex/cc_cg_proof.con. +inline "cic:/CoRN/complex/CComplex/cc_cg_proof.con". -inline cic:/CoRN/complex/CComplex/cc_cr_dist.con. +inline "cic:/CoRN/complex/CComplex/cc_cr_dist.con". -inline cic:/CoRN/complex/CComplex/cc_cr_non_triv.con. +inline "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con". -inline cic:/CoRN/complex/CComplex/cc_cgroup.con. +inline "cic:/CoRN/complex/CComplex/cc_cgroup.con". -inline cic:/CoRN/complex/CComplex/cc_cabgroup.con. +inline "cic:/CoRN/complex/CComplex/cc_cabgroup.con". -inline cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con. +inline "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con". -inline cic:/CoRN/complex/CComplex/cc_mult_commutes.con. +inline "cic:/CoRN/complex/CComplex/cc_mult_commutes.con". -inline cic:/CoRN/complex/CComplex/cc_isCRing.con. +inline "cic:/CoRN/complex/CComplex/cc_isCRing.con". -inline cic:/CoRN/complex/CComplex/cc_cring.con. +inline "cic:/CoRN/complex/CComplex/cc_cring.con". -inline cic:/CoRN/complex/CComplex/cc_ap_zero.con. +inline "cic:/CoRN/complex/CComplex/cc_ap_zero.con". -inline cic:/CoRN/complex/CComplex/cc_inv_aid.con. +inline "cic:/CoRN/complex/CComplex/cc_inv_aid.con". (*#* If [x [~=] Zero] or [y [~=] Zero], then [x [/] x[^]2 [+] y[^]2 [~=] Zero] or [[--]y[/]x[^]2[+]y[^]2 [~=] Zero]. *) -inline cic:/CoRN/complex/CComplex/cc_inv_aid2.con. +inline "cic:/CoRN/complex/CComplex/cc_inv_aid2.con". (* REMARK KEPT FOR SENTIMENTAL REASONS... @@ -152,11 +152,11 @@ input (Re or Im) is NonZero (a Prop), we manage to construct the actual function. *) -inline cic:/CoRN/complex/CComplex/cc_recip.con. +inline "cic:/CoRN/complex/CComplex/cc_recip.con". -inline cic:/CoRN/complex/CComplex/cc_cfield_proof.con. +inline "cic:/CoRN/complex/CComplex/cc_cfield_proof.con". -inline cic:/CoRN/complex/CComplex/cc_Recip_proof.con. +inline "cic:/CoRN/complex/CComplex/cc_Recip_proof.con". (* UNEXPORTED Opaque cc_recip. @@ -166,27 +166,27 @@ Opaque cc_recip. Opaque cc_inv. *) -inline cic:/CoRN/complex/CComplex/cc_cfield.con. +inline "cic:/CoRN/complex/CComplex/cc_cfield.con". -inline cic:/CoRN/complex/CComplex/CC.con. +inline "cic:/CoRN/complex/CComplex/CC.con". (*#* Maps from reals to complex and vice-versa are defined, as well as conjugate, absolute value and the imaginary unit [I] *) -inline cic:/CoRN/complex/CComplex/cc_set_CC.con. +inline "cic:/CoRN/complex/CComplex/cc_set_CC.con". -inline cic:/CoRN/complex/CComplex/cc_IR.con. +inline "cic:/CoRN/complex/CComplex/cc_IR.con". -inline cic:/CoRN/complex/CComplex/CC_conj.con. +inline "cic:/CoRN/complex/CComplex/CC_conj.con". (* old def Definition CC_conj' : CC->CC := [z:CC_set] (CC_set_rec [_:CC_set]CC_set [Re0,Im0:IR] (Build_CC_set Re0 [--]Im0) z). *) -inline cic:/CoRN/complex/CComplex/AbsCC.con. +inline "cic:/CoRN/complex/CComplex/AbsCC.con". -inline cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con. +inline "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con". (* UNEXPORTED End Complex_Numbers. @@ -196,7 +196,7 @@ End Complex_Numbers. (* end hide *) -inline cic:/CoRN/complex/CComplex/II.con. +inline "cic:/CoRN/complex/CComplex/II.con". (*#* ** Properties of [II] *) @@ -204,43 +204,43 @@ inline cic:/CoRN/complex/CComplex/II.con. Section I_properties. *) -inline cic:/CoRN/complex/CComplex/I_square.con. +inline "cic:/CoRN/complex/CComplex/I_square.con". (* UNEXPORTED Hint Resolve I_square: algebra. *) -inline cic:/CoRN/complex/CComplex/I_square'.con. +inline "cic:/CoRN/complex/CComplex/I_square'.con". -inline cic:/CoRN/complex/CComplex/I_recip_lft.con. +inline "cic:/CoRN/complex/CComplex/I_recip_lft.con". -inline cic:/CoRN/complex/CComplex/I_recip_rht.con. +inline "cic:/CoRN/complex/CComplex/I_recip_rht.con". -inline cic:/CoRN/complex/CComplex/mult_I.con. +inline "cic:/CoRN/complex/CComplex/mult_I.con". -inline cic:/CoRN/complex/CComplex/I_wd.con. +inline "cic:/CoRN/complex/CComplex/I_wd.con". (*#* ** Properties of [Re] and [Im] *) -inline cic:/CoRN/complex/CComplex/calculate_norm.con. +inline "cic:/CoRN/complex/CComplex/calculate_norm.con". -inline cic:/CoRN/complex/CComplex/calculate_Re.con. +inline "cic:/CoRN/complex/CComplex/calculate_Re.con". -inline cic:/CoRN/complex/CComplex/calculate_Im.con. +inline "cic:/CoRN/complex/CComplex/calculate_Im.con". -inline cic:/CoRN/complex/CComplex/Re_wd.con. +inline "cic:/CoRN/complex/CComplex/Re_wd.con". -inline cic:/CoRN/complex/CComplex/Im_wd.con. +inline "cic:/CoRN/complex/CComplex/Im_wd.con". -inline cic:/CoRN/complex/CComplex/Re_resp_plus.con. +inline "cic:/CoRN/complex/CComplex/Re_resp_plus.con". -inline cic:/CoRN/complex/CComplex/Re_resp_inv.con. +inline "cic:/CoRN/complex/CComplex/Re_resp_inv.con". -inline cic:/CoRN/complex/CComplex/Im_resp_plus.con. +inline "cic:/CoRN/complex/CComplex/Im_resp_plus.con". -inline cic:/CoRN/complex/CComplex/Im_resp_inv.con. +inline "cic:/CoRN/complex/CComplex/Im_resp_inv.con". -inline cic:/CoRN/complex/CComplex/cc_calculate_square.con. +inline "cic:/CoRN/complex/CComplex/cc_calculate_square.con". (* UNEXPORTED End I_properties. @@ -261,27 +261,27 @@ Hint Resolve I_wd Re_wd Im_wd: algebra_c. Section Conj_properties. *) -inline cic:/CoRN/complex/CComplex/CC_conj_plus.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_plus.con". -inline cic:/CoRN/complex/CComplex/CC_conj_mult.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_mult.con". (* UNEXPORTED Hint Resolve CC_conj_mult: algebra. *) -inline cic:/CoRN/complex/CComplex/CC_conj_strext.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_strext.con". -inline cic:/CoRN/complex/CComplex/CC_conj_conj.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_conj.con". -inline cic:/CoRN/complex/CComplex/CC_conj_zero.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_zero.con". -inline cic:/CoRN/complex/CComplex/CC_conj_one.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_one.con". (* UNEXPORTED Hint Resolve CC_conj_one: algebra. *) -inline cic:/CoRN/complex/CComplex/CC_conj_nexp.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_nexp.con". (* UNEXPORTED End Conj_properties. @@ -298,51 +298,51 @@ Hint Resolve CC_conj_plus CC_conj_mult CC_conj_nexp CC_conj_conj Section cc_IR_properties. *) -inline cic:/CoRN/complex/CComplex/Re_cc_IR.con. +inline "cic:/CoRN/complex/CComplex/Re_cc_IR.con". -inline cic:/CoRN/complex/CComplex/Im_cc_IR.con. +inline "cic:/CoRN/complex/CComplex/Im_cc_IR.con". -inline cic:/CoRN/complex/CComplex/cc_IR_wd.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_wd.con". (* UNEXPORTED Hint Resolve cc_IR_wd: algebra_c. *) -inline cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con". -inline cic:/CoRN/complex/CComplex/cc_IR_mult.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_mult.con". (* UNEXPORTED Hint Resolve cc_IR_mult: algebra. *) -inline cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con". -inline cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con". -inline cic:/CoRN/complex/CComplex/cc_IR_plus.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_plus.con". (* UNEXPORTED Hint Resolve cc_IR_plus: algebra. *) -inline cic:/CoRN/complex/CComplex/cc_IR_minus.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_minus.con". -inline cic:/CoRN/complex/CComplex/cc_IR_zero.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_zero.con". (* UNEXPORTED Hint Resolve cc_IR_zero: algebra. *) -inline cic:/CoRN/complex/CComplex/cc_IR_one.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_one.con". (* UNEXPORTED Hint Resolve cc_IR_one: algebra. *) -inline cic:/CoRN/complex/CComplex/cc_IR_nring.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_nring.con". -inline cic:/CoRN/complex/CComplex/cc_IR_nexp.con. +inline "cic:/CoRN/complex/CComplex/cc_IR_nexp.con". (* UNEXPORTED End cc_IR_properties. @@ -367,17 +367,13 @@ Hint Resolve cc_IR_nring cc_IR_zero: algebra. (*#* ** [CC] has characteristic zero *) -(* INCLUDE -Transparent_algebra -*) +include "tactics/Transparent_algebra.ma". -inline cic:/CoRN/complex/CComplex/char0_CC.con. +inline "cic:/CoRN/complex/CComplex/char0_CC.con". -(* INCLUDE -Opaque_algebra -*) +include "tactics/Opaque_algebra.ma". -inline cic:/CoRN/complex/CComplex/poly_apzero_CC.con. +inline "cic:/CoRN/complex/CComplex/poly_apzero_CC.con". -inline cic:/CoRN/complex/CComplex/poly_CC_extensional.con. +inline "cic:/CoRN/complex/CComplex/poly_CC_extensional.con".