--- /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/tactics/RingReflection".
+
+include "CoRN.ma".
+
+(* $Id: RingReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *)
+
+(* begin hide *)
+
+include "algebra/CRings.ma".
+
+include "tactics/AlgReflection.ma".
+
+(* UNEXPORTED
+Section Ring_Interpretation_Function
+*)
+
+alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var".
+
+alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var".
+
+alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var".
+
+alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var".
+
+alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var".
+
+inline "cic:/CoRN/tactics/RingReflection/interpR.ind".
+
+inline "cic:/CoRN/tactics/RingReflection/wfR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/xexprR.ind".
+
+inline "cic:/CoRN/tactics/RingReflection/xforgetR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/xinterpR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con".
+
+inline "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR.ind".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR_var.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR_int.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR_plus.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR_mult.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fforgetR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR2interp.con".
+
+inline "cic:/CoRN/tactics/RingReflection/fexprR2wf.con".
+
+(* UNEXPORTED
+Opaque csg_crr.
+*)
+
+(* UNEXPORTED
+Opaque cm_crr.
+*)
+
+(* UNEXPORTED
+Opaque cg_crr.
+*)
+
+(* UNEXPORTED
+Opaque cr_crr.
+*)
+
+(* UNEXPORTED
+Opaque csf_fun.
+*)
+
+(* UNEXPORTED
+Opaque csbf_fun.
+*)
+
+(* UNEXPORTED
+Opaque csr_rel.
+*)
+
+(* UNEXPORTED
+Opaque cs_eq.
+*)
+
+(* UNEXPORTED
+Opaque cs_neq.
+*)
+
+(* UNEXPORTED
+Opaque cs_ap.
+*)
+
+(* UNEXPORTED
+Opaque cm_unit.
+*)
+
+(* UNEXPORTED
+Opaque csg_op.
+*)
+
+(* UNEXPORTED
+Opaque cg_inv.
+*)
+
+(* UNEXPORTED
+Opaque cg_minus.
+*)
+
+(* UNEXPORTED
+Opaque cr_one.
+*)
+
+(* UNEXPORTED
+Opaque cr_mult.
+*)
+
+(* UNEXPORTED
+Opaque nexp_op.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/refl_interpR.con".
+
+inline "cic:/CoRN/tactics/RingReflection/interpR_wd.con".
+
+(* UNEXPORTED
+End Ring_Interpretation_Function
+*)
+
+(* UNEXPORTED
+Section Ring_NormCorrect
+*)
+
+alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var".
+
+alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var".
+
+alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var".
+
+alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var".
+
+alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var".
+
+(* NOTATION
+Notation II := (interpR R val unop binop pfun).
+*)
+
+(*
+four kinds of exprs:
+
+ I (expr_int _)
+ V (expr_var _)
+ M (expr_mult V M)
+ I
+ P (expr_plus M P)
+ I
+
+M: sorted on V
+P: sorted on M, all M's not an I
+*)
+
+(* UNEXPORTED
+Opaque Zmult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con".
+
+(* UNEXPORTED
+Transparent Zmult.
+*)
+
+(* UNEXPORTED
+Opaque MI_mult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con".
+
+(* UNEXPORTED
+Transparent MI_mult.
+*)
+
+(* UNEXPORTED
+Opaque MV_mult MI_mult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con".
+
+(* UNEXPORTED
+Transparent MV_mult MI_mult.
+*)
+
+(* UNEXPORTED
+Opaque MV_mult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con".
+
+(* UNEXPORTED
+Transparent MV_mult.
+*)
+
+(* UNEXPORTED
+Opaque MM_plus.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con".
+
+(* UNEXPORTED
+Transparent MM_plus.
+*)
+
+(* UNEXPORTED
+Opaque PM_plus.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con".
+
+(* UNEXPORTED
+Transparent PM_plus.
+*)
+
+(* UNEXPORTED
+Opaque PM_plus MM_mult MI_mult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con".
+
+(* UNEXPORTED
+Opaque PM_mult.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con".
+
+(*
+Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
+Lemma FF_plus_corr_R : (e,f:expr; x,y:R)
+ (II e x)->(II f y)->(II (FF_plus e f) x[+]y).
+Cut (e1,e2,f1,f2:expr; x,y:R)
+ (II (expr_div e1 e2) x)
+ ->(II (expr_div f1 f2) y)
+ ->(II
+ (expr_div (PP_plus (PP_mult e1 f2) (PP_mult e2 f1))
+ (PP_mult e2 f2)) x[+]y).
+Cut (e,f:expr; x,y:R)(II e x)->(II f y)->(II (expr_plus e f) x[+]y).
+Intros H H0 e f.
+Elim e; Elim f; Intros; Simpl; Auto.
+Intros. Apply interpR_plus with x y; Algebra.
+Intros. Inversion H. Inversion H0.
+Apply interpR_div_one with x[+]y.
+Algebra.
+Apply interpR_wd with x0[*]One[+]One[*]x1.
+Apply PP_plus_corr_R; Apply PP_mult_corr_R; Auto;
+ Apply interpR_int with k:=`1`; Algebra.
+Step_final x0[+]x1.
+Apply interpR_wd with (One::R)[*]One; Algebra.
+Apply PP_mult_corr_R; Auto.
+Qed.
+
+Lemma FF_mult_corr_R : (e,f:expr; x,y:R)
+ (II e x)->(II f y)->(II (FF_mult e f) x[*]y).
+Cut (e1,e2,f1,f2:expr; x,y:R)
+ (II (expr_div e1 e2) x)
+ ->(II (expr_div f1 f2) y)
+ ->(II (expr_div (PP_mult e1 f1) (PP_mult e2 f2)) x[*]y).
+Cut (e,f:expr; x,y:R)(II e x)->(II f y)->(II (expr_mult e f) x[*]y).
+Intros H H0 e f.
+Elim e; Elim f; Intros; Simpl; Auto.
+Intros. Apply interpR_mult with x y; Algebra.
+Intros. Inversion H. Inversion H0.
+Apply interpR_div_one with x0[*]x1.
+Algebra.
+Apply PP_mult_corr_R; Auto.
+Apply interpR_wd with (One::R)[*]One; Algebra.
+Apply PP_mult_corr_R; Auto.
+Qed.
+
+Transparent FF_div.
+Lemma FF_div_corr_R : (e,f:expr; x:R)
+ (II (expr_div e f) x)->(II (FF_div e f) x).
+Intro e; Case e; Simpl; Auto.
+Intros e0 e1 f; Case f; Simpl; Auto.
+Intros.
+Inversion H; Simpl.
+Inversion H3; Inversion H5.
+Apply interpR_div_one with x1[*]One.
+astepl x1. Step_final x0.
+Apply PP_mult_corr_R; Auto.
+Apply interpR_wd with One[*]x2.
+Apply PP_mult_corr_R; Auto.
+Step_final x2.
+Qed.
+*)
+
+inline "cic:/CoRN/tactics/RingReflection/NormR_corr.con".
+
+inline "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con".
+
+(* UNEXPORTED
+End Ring_NormCorrect
+*)
+
+(* end hide *)
+
projects / helm.git / blobdiff