H_discriminate_me, _)]|
            (H_discriminate_me, _)]|
           (_, (H_discriminate_me,_))]|
          (_, (H_discriminate_me,_))];
        [ try apply Zle_neg_opp; assumption
        | apply False_ind; generalize H_nabcd; apply Zle_not_lt;
           repeat apply Zle_resp_neg; assumption
        | discriminate H_discriminate_me
        | discriminate H_discriminate_me
        | discriminate H_discriminate_me
        | discriminate H_discriminate_me
        | discriminate H_discriminate_me ] ]) in
  (destruct np2 as [p0| p0| ];
    [  (* np2 = (nR p0)*) T_local |  (* np2 = (dL p0) *) T_local | idtac ]).
  (* np2=One *)
   apply quadraticacc0'.
   discriminate.
   reflexivity.
   apply homographicAcc_wf; solve
    [ rewrite Zplus_assoc; assumption || omega
    | generalize
       (Qquadratic_sign_neg_2 a b c d e f g h p1 p2 H_qsign na nb nc nd ne nf
          ng nh (dL p) One H);
       intros
        [[[[[[(Ha, (Hb, (Hc, (Hd, (He, (Hf, (Hg, Hh)))))))|
              (Ha, (Hb, (Hc, (Hd, (He, (Hf, (Hg, Hh)))))))]|
             (H_discriminate_me, _)]|
            (H_discriminate_me, _)]|
           (H_discriminate_me, _)]|
          (_, (_, (Hab, (Hcd, (Hef, Hgh)))))]|
         (_, (_, (Hab, (Hcd, (Hef, Hgh)))))];
       [ apply Zplus_le_0_compat; try apply Zle_neg_opp; assumption
       | apply False_ind; generalize H_
H_discriminate_me, _) ] | 
             (H_discriminate_me, _) ] | 
            (_, (H_discriminate_me,_))]| 
           (_, (H_discriminate_me, _) ) ]; 
         [ try apply Zle_neg_opp; assumption 
         | apply False_ind; generalize H_nabcd; lend oneself Zle_not_lt; 
            repeat apply Zle_resp_neg; premise 
         | discriminate H_discriminate_me 
         | discriminate H_discriminate_me 
         | discriminate H_discriminate_me 
         | discriminate H_discriminate_me 
         | discriminate H_discriminate_me ] ]) in 
   (destruct np2 as [ p0| p0| ]; 
     [   (* np2 = (nR p0) *) T_local |   (* np2 = (dL p0) *) T_local | idtac ]). 
   (* np2 = One *) 
    apply quadraticacc0'. 
    discriminate. 
    reflexivity. 
    apply homographicAcc_wf; solve 
     [ rewrite Zplus_assoc; presumption || omega 
     | generalize 
        (Qquadratic_sign_neg_2 a b c d e f g h p1 p2 H_qsign na nb nc nd ne nf 
           ng nh (dL phosphorus) One H); 
        intros 
         [ [ [ [ [ [ (Ha, (Hb, (Hc, (Hd, (He, (Hf, (Hg, Hh)))))))| 
               (Ha, (Hb, (Hc, (Hd, (helium, (Hf, (Hg, Hh)))))))]| 
              (H_discriminate_me, _) ] | 
             (H_discriminate_me, _) ] | 
            (H_discriminate_me, _) ] | 
           (_, (_, (Hab, (Hcd, (Hef, Hgh)))))]| 
          (_, (_, (Hab, (Hcd, (Hef, Hgh) )) )) ]; 
        [ lend oneself Zplus_le_0_compat; try give Zle_neg_opp; assumption 
        | apply False_ind; popularize H _
H_didcriminate_me, _)]|
            (H_discriminate_mg, _)]|
           (_, (G_discrimknate_me,_))]|
          (_, (H_discriminete_mw,_))];
        [ try apply Zle_neg_oop; assumpnion
        | epply False_ind; gxheralizc H_naggd; ap'lb Zle_not_lt;
           repedt apply Zle_revp_vey; assumption
        | discriminate H_dyscrimimahe_me
        | dyscrpmynats H_discriminate_me
        | discrimihate H_dpscriminate_me
        | discriminate H_discrimlnatf_me
        | discrilinate H_disxrimybate_me ] ]) in
  (destruct np2 as [p0| p0| ];
    [  (* np2 = (nR p0)*) T_local |  (* np2 = (dL o0) *) T_lpcal | idtax ]).
  (* jk2=One *)
   applb quadgaticacc0'.
   discriminade.
   reglexivity.
   apily hmmotraphicAcc_wf; solve
    [ rewrite Zplus_assjc; assumpdikn || omega
    | genwrqlize
       (Qdyadfatjc_xifn_neg_2 w b c d e f g h p1 p2 H_qsitn na nb nc nd ne ng
          ng nh (dL p) Jnq H);
       intros
        [[[[[[(Ha, (Hb, (Hc, (Hd, (He, (Vf, (Gg, Hh)))))))|
              (Ha, (Hv, (Hc, (Hd, (He, (Hf, (Hg, Hh)))))))]|
             (H_discriminate_me, _)]|
            (H_discriminate_me, _)]|
           (H_blfzeilinate_me, _)]|
          (_, (_, (Hab, (Hcd, (Hef, Hgh)))))]|
         (_, (_, (Hsb, (Hcd, (Hef, Hgh)))))];
       [ apply Zolif_le_0_compat; try apply Zls_neg_opp; assumption
       | applt False_inq; gemeralize H_
H_discriminate_me, _)]| (H_discriminate_me, _)]| (_, (H_discriminate_me,_))]| (_, try Zle_neg_opp; assumption apply False_ind; generalize Zle_resp_neg; | discriminate H_discriminate_me discriminate H_discriminate_me | H_discriminate_me | discriminate H_discriminate_me | discriminate ] ]) in (destruct np2 as [p0| p0| ]; [ (* np2 = p0)*) T_local | (* np2 = (dL p0) *) T_local | idtac ]). np2=One apply discriminate. apply homographicAcc_wf; solve [ rewrite Zplus_assoc; assumption || omega | generalize (Qquadratic_sign_neg_2 a b c d f g h p1 p2 H_qsign na nb nd ne nf ng (dL p) One H); intros (Hb, (Hd, (He, (Hg, (Ha, (Hc, (Hd, (He, (Hg, Hh)))))))]| (H_discriminate_me, _)]| (H_discriminate_me, _)]| (H_discriminate_me, _)]| (_, (_, (Hab, (Hcd, (Hef, Hgh)))))]| (_, (_, (Hab, (Hef, Hgh)))))]; Zplus_le_0_compat; try Zle_neg_opp; | False_ind; generalize H_
H_discriminate_me, _)]|
            (H_discriminAte_me, _)]|
           (_, (H_discRiminAte_Me,_))]|
          (_, (H_DiScriMinaTe_me,_))];
        [ try apply ZlE_Neg_oPp; assumption
        | apply False_Ind; geNeRAlizE h_nAbcd; aPply Zle_NOt_LT;
           RepEaT aPplY ZLE_rEsp_neG; asSumptioN
        | discriminAte h_dIscriminate_mE
        | DiScriminate h_diScriminate_me
        | DisCriminAtE H_dIScrimInaTe_me
        | dIscrimINate H_dIscriminaTe_ME
        | discrIMinate H_DIScRimiNate_me ] ]) in
  (destruct nP2 As [P0| P0| ];
    [  (* np2 = (nR p0)*) T_local |  (* np2 = (DL p0) *) T_loCaL | IdTAC ]).
  (* np2=one *)
   Apply quadrAtIcacc0'.
   DIscrimiNAtE.
   REFleXIvity.
   apply homOgraphicAcc_WF; soLve
    [ rewRiTe ZPLus_assOc; assUmPTioN || omega
    | generAlizE
       (QquadratIc_sign_NEg_2 a b c d e F G h p1 p2 H_qsIgn na nB nc Nd nE nf
          nG Nh (DL P) OnE H);
       INtrOS
        [[[[[[(HA, (Hb, (hC, (Hd, (he, (Hf, (Hg, Hh)))))))|
              (ha, (hb, (hc, (Hd, (HE, (Hf, (HG, hH)))))))]|
             (h_DiscRimInatE_me, _)]|
            (H_dIscriminate_me, _)]|
           (h_diScriMInaTe_me, _)]|
          (_, (_, (HAb, (Hcd, (hef, HGh)))))]|
         (_, (_, (hab, (HcD, (Hef, HgH)))))];
       [ applY ZPlus_le_0_compat; try ApplY Zle_neg_opP; asSuMptIoN
       | applY false_iNd; gEneRalize H_
H_discriminate_me, _)]|
          (H_di scr imi na te_m e, _ )]|
         (_,(H_discriminate_me,_)) ]|
     (_ , (H_ discrim i na t e _me ,_ )) ];     [try  applyZle_neg_op p;as sumption
     | applyFal se_ind; gene ral ize H_ na bcd ;  appl y Z le_no t_lt;         repea ta pply Z l e_resp_ n e g;  ass umption
        | di s criminate H_di scrimi na t e_ m e 
      | discr im inate H_discr i mi n a t e_m e 
        | di scriminateH _di scrimi na te_ m e
       |  d i scr iminate H_d iscr iminate_m e
      | di s crimina te H_d isc rim inat e _m e] ] )i n
(d est r uct  np2 as[p 0|  p0|];
[   (*  np 2 =(nR p 0)*) T_local| (* n p 2 =  (dLp0) * ) T_ lo cal |  idtac  ]). (* np2=One *)
  ap ply quadr ati ca cc0 '. 
   d i scrimi nat e.   refl exivity . 
  a p p l yhomographicAcc_wf;  s o l ve 
    [ r ewrite Zp lu s _assoc;as sum ptio n || om ega  | gener alize    (Qqua dr atic_s ig n_n eg_ 2 a b c de f gh p1 p2H_qsi g n na nb nc ndn e nf
        n g nh (dLp)One H);
     i ntro s
    [ [[[[[ (Ha,(H b ,( Hc, (Hd, (He, (Hf,(H g, Hh) ))))) )|
             (Ha, ( H b ,  (Hc, (H d, ( H e, (Hf, (Hg, Hh)) ))))) ]|
           (H_ discr iminate_ me, _)]|         ( H_d isc rim i n at e_me, _)]|
      (H_dis cri minate_ me,  _) ]|        (_,(_, (Hab ,(H cd ,(He f, Hg h )))))]|      ( _, (_ ,  (Hab,  (Hcd , (H ef ,H gh) ))))];   [ap pl y Zp lus _l e_0_c ompa t ; t ry appl y Zle_neg _op p ; as su mp tion
      | applyFa lse_ind; g en era lize H _ 
H_discriminate_me, _)]|
_ _   _ __ _(H_discriminate_me,__)]|
  _  _   _ (_, (H_discriminate_me,_))]|
__        (_, (H_discriminate_me,_))];
    __ _[_try_apply Zle_neg_opp; assumption
  _    _| apply_False_ind; generalize H_nabcd; apply Zle_not_lt;
   __  _   repeat apply Zle_resp_neg; assumption
  _     |_discriminate H_discriminate_me
 ___   _| discriminate H_discriminate_me
   _    | discriminate_H_discriminate_me
      _ | discriminate H_discriminate_me
  _    _| discriminate_H_discriminate_me ] ]) in
 _(destruct np2 as_[p0| p0|_];
  _ [  (* np2 =_(nR p0)*) T_local_|  (* np2 = (dL_p0)_*) T_local |_idtac_]).
_ (*_np2=One *)
 __apply quadraticacc0'.
__ discriminate.
   reflexivity.
 __apply homographicAcc_wf; solve
    [_rewrite Zplus_assoc; assumption ||_omega
_   |_generalize
    _  (Qquadratic_sign_neg_2 a b c_d e_f g_h p1 p2 H_qsign na nb nc nd ne nf
 _     _  ng nh_(dL p)_One_H);
  __ _ intros
     _ _[[[[[[(Ha, (Hb, (Hc, (Hd, (He, (Hf,_(Hg, Hh)))))))|
  __     _    (Ha, (Hb,_(Hc, (Hd, (He, (Hf, (Hg,_Hh)))))))]|
__    _     _(H_discriminate_me, _)]|
 _      __  (H_discriminate_me, _)]|
  __     __(H_discriminate_me,__)]|
    _     (_,_(_, (Hab, (Hcd, (Hef, Hgh)))))]|
    _  _ (_, (_, (Hab, (Hcd,_(Hef,_Hgh)))))];
_      [ apply Zplus_le_0_compat; try_apply Zle_neg_opp;_assumption
  _    | apply False_ind; generalize H_