--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/CoRN".
+
+include "preamble.ma".
+
+(* From algebra/Basics ****************************************************)
+
+(* NOTATION
+Notation Pair := (pair (B:=_)).
+*)
+
+(* NOTATION
+Notation Proj1 := (proj1 (B:=_)).
+*)
+
+(* NOTATION
+Notation Proj2 := (proj2 (B:=_)).
+*)
+
+coercion cic:/Coq/ZArith/BinInt/Z_of_nat.con 0 (* compounds *).
+
+(* From algebra/CAbGroups *************************************************)
+
+coercion cic:/CoRN/algebra/CAbGroups/cag_crr.con 0 (* compounds *).
+
+(* From algebra/CAbMonoids ************************************************)
+
+coercion cic:/CoRN/algebra/CAbMonoids/cam_crr.con 0 (* compounds *).
+
+(* From algebra/CFields ***************************************************)
+
+coercion cic:/CoRN/algebra/CFields/cf_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation "x [/] y [//] Hy" := (cf_div x y Hy) (at level 80).
+*)
+
+(* NOTATION
+Notation "{1/} x" := (Frecip x) (at level 2, right associativity).
+*)
+
+(* NOTATION
+Infix "{/}" := Fdiv (at level 41, no associativity).
+*)
+
+(* From algebra/CGroups ***************************************************)
+
+coercion cic:/CoRN/algebra/CGroups/cg_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation "[--] x" := (cg_inv x) (at level 2, right associativity).
+*)
+
+(* NOTATION
+Infix "[-]" := cg_minus (at level 50, left associativity).
+*)
+
+(* NOTATION
+Notation "{--} x" := (Finv x) (at level 2, right associativity).
+*)
+
+(* NOTATION
+Infix "{-}" := Fminus (at level 50, left associativity).
+*)
+
+(* From algebra/CLogic ****************************************************)
+
+(* NOTATION
+Infix "IFF" := Iff (at level 60, right associativity).
+*)
+
+(* NOTATION
+Infix "or" := COr (at level 85, right associativity).
+*)
+
+(* NOTATION
+Infix "and" := CAnd (at level 80, right associativity).
+*)
+
+(* NOTATION
+Notation "{ x : A | P }" := (sigT (fun x : A => P):CProp)
+ (at level 0, x at level 99) : type_scope.
+*)
+
+(* NOTATION
+Notation "{ x : A | P | Q }" :=
+ (sig2T A (fun x : A => P) (fun x : A => Q)) (at level 0, x at level 99) :
+ type_scope.
+*)
+
+(* NOTATION
+Notation ProjT1 := (proj1_sigT _ _).
+*)
+
+(* NOTATION
+Notation ProjT2 := (proj2_sigT _ _).
+*)
+
+(* From algebra/CMonoids **************************************************)
+
+coercion cic:/CoRN/algebra/CMonoids/cm_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation Zero := (cm_unit _).
+*)
+
+(* From algebra/COrdAbs ***************************************************)
+
+(* NOTATION
+Notation ZeroR := (Zero:R).
+*)
+
+(* NOTATION
+Notation AbsBig := (absBig _).
+*)
+
+(* From algebra/COrdCauchy ************************************************)
+
+coercion cic:/CoRN/algebra/COrdCauchy/CS_seq.con 0 (* compounds *).
+
+(* From algebra/COrdFields ************************************************)
+
+coercion cic:/CoRN/algebra/COrdFields/cof_crr.con 0 (* compounds *).
+
+(* NOTATION
+Infix "[<]" := cof_less (at level 70, no associativity).
+*)
+
+(* NOTATION
+Infix "[>]" := greater (at level 70, no associativity).
+*)
+
+(* NOTATION
+Infix "[<=]" := leEq (at level 70, no associativity).
+*)
+
+(* NOTATION
+Notation " x [/]OneNZ" := (x[/] One[//]ring_non_triv _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwoNZ" := (x[/] Two[//]two_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]ThreeNZ" := (x[/] Three[//]three_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]FourNZ" := (x[/] Four[//]four_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]SixNZ" := (x[/] Six[//]six_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]EightNZ" := (x[/] Eight[//]eight_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]NineNZ" := (x[/] Nine[//]nine_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwelveNZ" := (x[/] Twelve[//]twelve_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]SixteenNZ" := (x[/] Sixteen[//]sixteen_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]EighteenNZ" := (x[/] Eighteen[//]eighteen_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwentyFourNZ" := (x[/] TwentyFour[//]twentyfour_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]FortyEightNZ" := (x[/] FortyEight[//]fortyeight_ap_zero _) (at level 20).
+*)
+
+(* From algebra/COrdFields2 ***********************************************)
+
+(* NOTATION
+Notation ZeroR := (Zero:R).
+*)
+
+(* NOTATION
+Notation OneR := (One:R).
+*)
+
+(* From algebra/CPoly_ApZero **********************************************)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* From algebra/CPoly_Degree **********************************************)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation FX := (cpoly_cring F).
+*)
+
+(* From algebra/CPoly_NthCoeff ********************************************)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* From algebra/CPolynomials **********************************************)
+
+(* NOTATION
+Infix "[+X*]" := cpoly_linear_fun' (at level 50, left associativity).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring CR).
+*)
+
+(* NOTATION
+Infix "!" := cpoly_apply_fun (at level 1, no associativity).
+*)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* NOTATION
+Notation Cpoly := (cpoly CR).
+*)
+
+(* NOTATION
+Notation Cpoly_zero := (cpoly_zero CR).
+*)
+
+(* NOTATION
+Notation Cpoly_linear := (cpoly_linear CR).
+*)
+
+(* NOTATION
+Notation Cpoly_cring := (cpoly_cring CR).
+*)
+
+(* From algebra/CRings ****************************************************)
+
+coercion cic:/CoRN/algebra/CRings/cr_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation One := (cr_one _).
+*)
+
+(* NOTATION
+Infix "[*]" := cr_mult (at level 40, left associativity).
+*)
+
+(* NOTATION
+Notation "x [^] n" := (nexp_op _ n x) (at level 20).
+*)
+
+(* NOTATION
+Notation Two := (nring 2).
+*)
+
+(* NOTATION
+Notation Three := (nring 3).
+*)
+
+(* NOTATION
+Notation Four := (nring 4).
+*)
+
+(* NOTATION
+Notation Six := (nring 6).
+*)
+
+(* NOTATION
+Notation Eight := (nring 8).
+*)
+
+(* NOTATION
+Notation Twelve := (nring 12).
+*)
+
+(* NOTATION
+Notation Sixteen := (nring 16).
+*)
+
+(* NOTATION
+Notation Nine := (nring 9).
+*)
+
+(* NOTATION
+Notation Eighteen := (nring 18).
+*)
+
+(* NOTATION
+Notation TwentyFour := (nring 24).
+*)
+
+(* NOTATION
+Notation FortyEight := (nring 48).
+*)
+
+(* NOTATION
+Infix "{*}" := Fmult (at level 40, left associativity).
+*)
+
+(* NOTATION
+Infix "{**}" := Fscalmult (at level 40, left associativity).
+*)
+
+(* NOTATION
+Infix "{^}" := Fnth (at level 30, right associativity).
+*)
+
+(* From algebra/CSemiGroups ***********************************************)
+
+coercion cic:/CoRN/algebra/CSemiGroups/csg_crr.con 0 (* compounds *).
+
+(* NOTATION
+Infix "[+]" := csg_op (at level 50, left associativity).
+*)
+
+(* NOTATION
+Infix "{+}" := Fplus (at level 50, left associativity).
+*)
+
+(* From algebra/CSetoidFun ************************************************)
+
+(* NOTATION
+Notation Conj := (conjP _).
+*)
+
+coercion cic:/CoRN/algebra/CSetoidFun/bpfpfun.con 0 (* compounds *).
+
+(* NOTATION
+Notation BDom := (bpfdom _ _).
+*)
+
+coercion cic:/CoRN/algebra/CSetoidFun/pfpfun.con 0 (* compounds *).
+
+(* NOTATION
+Notation Dom := (pfdom _).
+*)
+
+(* NOTATION
+Notation Part := (pfpfun _).
+*)
+
+(* NOTATION
+Notation "[-C-] x" := (Fconst x) (at level 2, right associativity).
+*)
+
+(* NOTATION
+Notation FId := (Fid _).
+*)
+
+(* NOTATION
+Infix "[o]" := Fcomp (at level 65, no associativity).
+*)
+
+(* NOTATION
+Notation Prj1 := (prj1 _ _ _ _).
+*)
+
+(* NOTATION
+Notation Prj2 := (prj2 _ _ _ _).
+*)
+
+(* From algebra/CSetoids **************************************************)
+
+coercion cic:/CoRN/algebra/CSetoids/cs_crr.con 0 (* compounds *).
+
+(* NOTATION
+Infix "[=]" := cs_eq (at level 70, no associativity).
+*)
+
+(* NOTATION
+Infix "[#]" := cs_ap (at level 70, no associativity).
+*)
+
+(* NOTATION
+Infix "[~=]" := cs_neq (at level 70, no associativity).
+*)
+
+coercion cic:/CoRN/algebra/CSetoids/csp_pred.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/csp'_pred.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/csr_rel.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/Ccsr_rel.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/csf_fun.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/csbf_fun.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/un_op_fun.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/bin_op_bin_fun.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/outer_op_bin_fun.con 0 (* compounds *).
+
+coercion cic:/CoRN/algebra/CSetoids/scs_elem.con 0 (* compounds *).
+
+(* From algebra/CVectorSpace **********************************************)
+
+coercion cic:/CoRN/algebra/CVectorSpace/vs_vs.con 0 (* compounds *).
+
+(* NOTATION
+Infix "[']" := vs_op (at level 30, no associativity).
+*)
+
+(* From algebra/Expon *****************************************************)
+
+(* NOTATION
+Notation "( x [//] Hx ) [^^] n" := (zexp x Hx n) (at level 0).
+*)
+
+(* From complex/CComplex **************************************************)
+
+(* NOTATION
+Notation CCX := (cpoly_cring CC).
+*)
+
+(* NOTATION
+Infix "[+I*]" := cc_set_CC (at level 48, no associativity).
+*)
+
+(* From fta/CC_Props ******************************************************)
+
+coercion cic:/CoRN/fta/CC_Props/CC_seq.con 0 (* compounds *).
+
+(* From fta/FTAreg ********************************************************)
+
+coercion cic:/CoRN/fta/FTAreg/z_el.con 0 (* compounds *).
+
+coercion cic:/CoRN/fta/FTAreg/Kntup.con 0 (* compounds *).
+
+(* From ftc/FTC ***********************************************************)
+
+(* NOTATION
+Notation "[-S-] F" := (Fprim F) (at level 20).
+*)
+
+(* From ftc/Integral ******************************************************)
+
+(* NOTATION
+Notation Integral := (integral _ _ Hab).
+*)
+
+(* From ftc/MoreIntervals *************************************************)
+
+coercion cic:/CoRN/ftc/MoreIntervals/iprop.con 0 (* compounds *).
+
+(* From ftc/Partitions ****************************************************)
+
+coercion cic:/CoRN/ftc/Partitions/Pts.con 0 (* compounds *).
+
+(* From ftc/RefLemma ******************************************************)
+
+(* NOTATION
+Notation g := RL_g.
+*)
+
+(* NOTATION
+Notation h := RL_h.
+*)
+
+(* NOTATION
+Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfP _ _)).
+*)
+
+(* NOTATION
+Notation just2 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfQ _ _)).
+*)
+
+(* NOTATION
+Notation just := (fun z => incF _ (Pts_part_lemma _ _ _ _ _ _ z _ _)).
+*)
+
+(* From ftc/RefSeparated **************************************************)
+
+(* NOTATION
+Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ gP _ _)).
+*)
+
+(* NOTATION
+Notation just2 :=
+ (incF _ (Pts_part_lemma _ _ _ _ _ _ sep__sep_points_lemma _ _)).
+*)
+
+(* From ftc/RefSeparating *************************************************)
+
+(* NOTATION
+Notation m := RS'_m.
+*)
+
+(* NOTATION
+Notation h := RS'_h.
+*)
+
+(* NOTATION
+Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ gP _ _)).
+*)
+
+(* NOTATION
+Notation just2 :=
+ (incF _ (Pts_part_lemma _ _ _ _ _ _ sep__part_pts_in_Partition _ _)).
+*)
+
+(* From ftc/Rolle *********************************************************)
+
+(* NOTATION
+Notation cp := (compact_part a b Hab' d Hd).
+*)
+
+(* From ftc/TaylorLemma ***************************************************)
+
+(* NOTATION
+Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a).
+*)
+
+(* NOTATION
+Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b).
+*)
+
+(* From ftc/WeakIVT *******************************************************)
+
+(* NOTATION
+Infix "**" := prodT (at level 20).
+*)
+
+(* From metrics/CMetricSpaces *********************************************)
+
+coercion cic:/CoRN/metrics/CMetricSpaces/scms_crr.con 0 (* compounds *).
+
+(* From metrics/CPseudoMSpaces ********************************************)
+
+coercion cic:/CoRN/metrics/CPseudoMSpaces/cms_crr.con 0 (* compounds *).
+
+(* NOTATION
+Infix "[-d]" := cms_d (at level 68, left associativity).
+*)
+
+(* From model/structures/Nsec *********************************************)
+
+(* NOTATION
+Infix "{#N}" := ap_nat (no associativity, at level 90).
+*)
+
+(* From model/structures/Qsec *********************************************)
+
+(* NOTATION
+Infix "{=Q}" := Qeq (no associativity, at level 90).
+*)
+
+(* NOTATION
+Infix "{#Q}" := Qap (no associativity, at level 90).
+*)
+
+(* NOTATION
+Infix "{<Q}" := Qlt (no associativity, at level 90).
+*)
+
+(* NOTATION
+Infix "{+Q}" := Qplus (no associativity, at level 85).
+*)
+
+(* NOTATION
+Infix "{*Q}" := Qmult (no associativity, at level 80).
+*)
+
+(* NOTATION
+Notation "{-Q}" := Qopp (at level 1, left associativity).
+*)
+
+coercion cic:/CoRN/model/structures/Qsec/inject_Z.con 0 (* compounds *).
+
+(* From model/structures/Zsec *********************************************)
+
+(* NOTATION
+Infix "{#Z}" := ap_Z (no associativity, at level 90).
+*)
+
+coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *).
+
+(* From reals/Bridges_LUB *************************************************)
+
+(* NOTATION
+Notation "( p , q )" := (pairT p q).
+*)
+
+(* From reals/CMetricFields ***********************************************)
+
+coercion cic:/CoRN/reals/CMetricFields/cmf_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation MAbs := (cmf_abs _).
+*)
+
+coercion cic:/CoRN/reals/CMetricFields/MCS_seq.con 0 (* compounds *).
+
+(* From reals/CReals ******************************************************)
+
+coercion cic:/CoRN/reals/CReals/crl_crr.con 0 (* compounds *).
+
+(* From reals/CauchySeq ***************************************************)
+
+(* NOTATION
+Notation PartIR := (PartFunct IR).
+*)
+
+(* NOTATION
+Notation ProjIR1 := (prj1 IR _ _ _).
+*)
+
+(* NOTATION
+Notation ProjIR2 := (prj2 IR _ _ _).
+*)
+
+(* NOTATION
+Notation ZeroR := (Zero:IR).
+*)
+
+(* NOTATION
+Notation OneR := (One:IR).
+*)
+
+(* From reals/Cauchy_CReals ***********************************************)
+
+(* NOTATION
+Notation "'R_COrdField''" := (R_COrdField F).
+*)
+
+(* From reals/Intervals ***************************************************)
+
+(* NOTATION
+Notation Compact := (compact _ _).
+*)
+
+(* NOTATION
+Notation FRestr := (Frestr (compact_wd _ _ _)).
+*)
+
+(* From reals/Q_dense *****************************************************)
+
+coercion cic:/CoRN/reals/Q_dense/pair_crr.con 0 (* compounds *).
+
+(* NOTATION
+Notation "( A , B )" := (pairT A B).
+*)
+
+(* From reals/Q_in_CReals *************************************************)
+
+coercion cic:/Coq/NArith/BinPos/nat_of_P.con 0 (* compounds *).
+
+(* From reals/R_morphism **************************************************)
+
+coercion cic:/CoRN/reals/R_morphism/map.con 0 (* compounds *).
+
+(* From tactics/FieldReflection *******************************************)
+
+(* NOTATION
+Notation II := (interpF F val unop binop pfun).
+*)
+
+(* From tactics/GroupReflection *******************************************)
+
+(* NOTATION
+Notation II := (interpG G val unop binop pfun).
+*)
+
+(* From tactics/RingReflection ********************************************)
+
+(* NOTATION
+Notation II := (interpR R val unop binop pfun).
+*)
+
+(* From transc/RealPowers *************************************************)
+
+(* NOTATION
+Notation "x [!] y [//] Hy" := (power x y Hy) (at level 20).
+*)
+
+(* NOTATION
+Notation "F {!} G" := (FPower F G) (at level 20).
+*)
+
+(* From devel/loeb/per/lst2fun ********************************************)
+
+coercion cic:/CoRN/devel/loeb/per/lst2fun/F_crr.con 0 (* compounds *).
+
+coercion cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con 0 (* compounds *).
+
projects / helm.git / blobdiff