File "/tmp/.coq-native/Ntmpychg3keq.native", line 1:
Error: /github/workspace/builds/coq/coq-failing/_install_ci/lib/coq/../coq-core/kernel/nativevalues.cmi
       is not a compiled interface for this version of OCaml.
It seems to be for an older version of OCaml.
Error: Native compiler exited with status 2

Declare ML Module "ltac_plugin".
Module Export AdmitTactic.
Module Import LocalFalse.
Inductive False := .
End LocalFalse.
Axiom proof_admitted : False.
Tactic Notation "admit" := abstract case proof_admitted.
End AdmitTactic.
Require Coq.ssr.ssreflect.
Require Coq.ssr.ssrfun.
Require Coq.ssr.ssrbool.
Require Coq.ZArith.ZArith.
Require Coq.QArith.QArith.
Require Coq.Strings.String.
Require Coq.Init.Ltac.
Require Coq.Bool.Bool.
Require Coq.Floats.PrimFloat.
Require Coq.Numbers.Cyclic.Int63.PrimInt63.
Require elpi.elpi.
Require HB.structures.
Require HB.examples.demo2.classical.

Import Coq.ssr.ssreflect Coq.ssr.ssrfun Coq.ssr.ssrbool Coq.ZArith.ZArith Coq.QArith.QArith.
Import HB.structures.
Import HB.examples.demo2.classical.

Declare Scope hb_scope.
Delimit Scope hb_scope with G.

Local Open Scope classical_set_scope.
Local Open Scope hb_scope.

Module Stage10.

HB.mixin Record AddAG_of_TYPE A := {
  zero : A;
  add : A -> A -> A;
  opp : A -> A;
  addrA : associative add;
  addrC : commutative add;
  add0r : left_id zero add;
  addNr : left_inverse zero opp add;
}.
HB.structure Definition AddAG := { A of AddAG_of_TYPE A }.

Notation "0" := zero : hb_scope.
Infix "+" := (@add _) : hb_scope.
Notation "- x" := (@opp _ x) : hb_scope.
Notation "x - y" := (x + - y) : hb_scope.

(* Theory *)

Section AddAGTheory.
Variable A : AddAG.type.
Implicit Type (x : A).

Lemma addr0 : right_id (@zero A) add.
Proof. by move=> x; rewrite addrC add0r. Qed.

Lemma addrN : right_inverse (@zero A) opp add.
Proof. by move=> x; rewrite addrC addNr. Qed.

Lemma subrr x : x - x = 0.
Proof. by rewrite addrN. Qed.

Lemma addrK : right_loop (@opp A) (@add A).
Proof. by move=> x y; rewrite -addrA subrr addr0. Qed.

Lemma addKr : left_loop (@opp A) (@add A).
Proof. by move=> x y; rewrite addrA addNr add0r. Qed.

Lemma addrNK : rev_right_loop (@opp A) (@add A).
Proof. by move=> y x; rewrite -addrA addNr addr0. Qed.

Lemma addNKr : rev_left_loop (@opp A) (@add A).
Proof. by move=> x y; rewrite addrA subrr add0r. Qed.

Lemma addrAC : right_commutative (@add A).
Proof. by move=> x y z; rewrite -!addrA [y + z]addrC. Qed.

Lemma addrCA : left_commutative (@add A).
Proof. by move=> x y z; rewrite !addrA [x + y]addrC. Qed.

Lemma addrACA : interchange (@add A) add.
Proof. by move=> x y z t; rewrite !addrA [x + y + z]addrAC. Qed.

Lemma opprK : involutive (@opp A).
Proof. by move=> x; apply: (can_inj (addrK (- x))); rewrite addNr addrN. Qed.

Lemma opprD x y : - (x + y) = - x - y.
Proof.
apply: (can_inj (addKr (x + y))).
by rewrite subrr addrACA !subrr addr0.
Qed.

Lemma opprB x y : - (x - y) = y - x.
Proof. by rewrite opprD opprK addrC. Qed.

End AddAGTheory.

HB.mixin Record Ring_of_AddAG A of AddAG A := {
  one : A;
  mul : A -> A -> A;
  mulrA : associative mul;
  mulr1 : left_id one mul;
  mul1r : right_id one mul;
  mulrDl : left_distributive mul add;
  mulrDr : right_distributive mul add;
}.
HB.factory Record Ring_of_TYPE A := {
  zero : A;
  one : A;
  add : A -> A -> A;
  opp : A -> A;
  mul : A -> A -> A;
  addrA : associative add;
  addrC : commutative add;
  add0r : left_id zero add;
  addNr : left_inverse zero opp add;
  mulrA : associative mul;
  mul1r : left_id one mul;
  mulr1 : right_id one mul;
  mulrDl : left_distributive mul add;
  mulrDr : right_distributive mul add;
}.

HB.builders Context A (a : Ring_of_TYPE A).

  HB.instance
  Definition to_AddAG_of_TYPE := AddAG_of_TYPE.Build A
    _ _ _ addrA addrC add0r addNr.

  HB.instance
  Definition to_Ring_of_AddAG :=
    Ring_of_AddAG.Build A _ _ mulrA mul1r
      mulr1 mulrDl mulrDr.

HB.end.

HB.structure Definition Ring := { A of Ring_of_TYPE A }.

Notation "1" := one : hb_scope.
Infix "*" := (@mul _) : hb_scope.

HB.mixin Record Topological T := {
  open : (T -> Prop) -> Prop;
  open_setT : open setT;
  open_bigcup : forall {I} (D : set I) (F : I -> set T),
    (forall i, D i -> open (F i)) -> open (\bigcup_(i in D) F i);
  open_setI : forall X Y : set T, open X -> open Y -> open (setI X Y);
}.
HB.structure Definition TopologicalSpace := { A of Topological A }.

Hint Extern 0 (open setT) => now apply: open_setT : core.

HB.factory Record TopologicalBase T := {
  open_base : set (set T);
  open_base_covers : setT `<=` \bigcup_(X in open_base) X;
  open_base_cup : forall X Y : set T, open_base X -> open_base Y ->
    forall z, (X `&` Y) z -> exists2 Z, open_base Z & Z z /\ Z `<=` X `&` Y
}.

HB.builders Context T (a : TopologicalBase T).

  Definition open_of : (T -> Prop) -> Prop :=
    [set A | exists2 D, D `<=` open_base & A = \bigcup_(X in D) X].

  Lemma open_of_setT : open_of setT.  Proof.
  exists open_base; rewrite // predeqE => x; split=> // _.
  by apply: open_base_covers.
  Qed.

  Lemma open_of_bigcup {I} (D : set I) (F : I -> set T) :
    (forall i, D i -> open_of (F i)) -> open_of (\bigcup_(i in D) F i).
  Proof. Admitted.

  Lemma open_of_cap X Y : open_of X -> open_of Y -> open_of (X `&` Y).
  Proof. Admitted.

  HB.instance
  Definition to_Topological :=
    Topological.Build T _ open_of_setT (@open_of_bigcup) open_of_cap.

HB.end.

Section ProductTopology.
  Variables (T1 T2 : TopologicalSpace.type).

  Definition prod_open_base :=
    [set A | exists (A1 : set T1) (A2 : set T2),
      open A1 /\ open A2 /\ A = setM A1 A2].

  Lemma prod_open_base_covers : setT `<=` \bigcup_(X in prod_open_base) X.
  Proof.
  move=> X _; exists setT => //; exists setT, setT; do ?split.
  - exact: open_setT.
  - exact: open_setT.
  - by rewrite predeqE.
  Qed.

  Lemma prod_open_base_setU X Y :
    prod_open_base X -> prod_open_base Y ->
      forall z, (X `&` Y) z ->
        exists2 Z, prod_open_base Z & Z z /\ Z `<=` X `&` Y.
  Proof.
  move=> [A1 [A2 [A1open [A2open ->]]]] [B1 [B2 [B1open [B2open ->]]]].
  move=> [z1 z2] [[/=Az1 Az2] [/= Bz1 Bz2]].
  exists ((A1 `&` B1) `*` (A2 `&` B2)).
    by eexists _, _; do ?[split; last first]; apply: open_setI.
  by split => // [[x1 x2] [[/=Ax1 Bx1] [/=Ax2 Bx2]]].
  Qed.

  HB.instance Definition prod_topology :=
    TopologicalBase.Build (T1 * T2)%type _ prod_open_base_covers prod_open_base_setU.

End ProductTopology.

Definition continuous {T T' : TopologicalSpace.type} (f : T -> T') :=
  forall B : set T', open B -> open (f@^-1` B).

Definition continuous2 {T T' T'': TopologicalSpace.type}
  (f : T -> T' -> T'') := continuous (fun xy => f xy.1 xy.2).

HB.mixin Record JoinTAddAG T of AddAG_of_TYPE T & Topological T := {
  add_continuous : continuous2 (add : T -> T -> T);
  opp_continuous : continuous (opp : T -> T)
}.

HB.structure Definition TAddAG := { A of Topological A & AddAG_of_TYPE A & JoinTAddAG A }.

(* Instance *)

HB.instance Definition Z_ring_axioms :=
  Ring_of_TYPE.Build Z 0%Z 1%Z Z.add Z.opp Z.mul
    Z.add_assoc Z.add_comm Z.add_0_l Z.add_opp_diag_l
    Z.mul_assoc Z.mul_1_l Z.mul_1_r
    Z.mul_add_distr_r Z.mul_add_distr_l.

Example test1 (m n : Z) : (m + n) - n + 0 = m.
Proof. by rewrite addrK addr0. Qed.
Import Qcanon.
Search _ Qc "plus" "opp".

Lemma Qcplus_opp_l q : - q + q = 0.
Proof. by rewrite Qcplus_comm Qcplus_opp_r. Qed.

HB.instance Definition Qc_ring_axioms :=
  Ring_of_TYPE.Build Qc 0%Qc 1%Qc Qcplus Qcopp Qcmult
    Qcplus_assoc Qcplus_comm Qcplus_0_l Qcplus_opp_l
    Qcmult_assoc Qcmult_1_l Qcmult_1_r
    Qcmult_plus_distr_l Qcmult_plus_distr_r.

Obligation Tactic := idtac.
Definition Qcopen_base : set (set Qc) :=
  [set A | exists a b : Qc, forall z, A z <-> a < z /\ z < b].
Program Definition QcTopological := TopologicalBase.Build Qc Qcopen_base _ _.
Next Obligation.
move=> x _; exists [set y | x - 1 < y < x + 1].
  by exists (x - 1), (x + 1).
split; rewrite Qclt_minus_iff.
  by rewrite -[_ + _]/(x - (x - 1))%G opprB addrCA subrr.
by rewrite -[_ + _]/(x + 1 - x)%G addrAC subrr.
Qed.
Next Obligation.
move=> X Y [aX [bX Xeq]] [aY [bY Yeq]] z [/Xeq [aXz zbX] /Yeq [aYz zbY]].
Admitted.

HB.instance Definition _ :  TopologicalBase Qc := QcTopological.

Program Definition QcJoinTAddAG := JoinTAddAG.Build Qc _ _.
Next Obligation. Admitted.
Next Obligation. Admitted.

HB.instance Definition _ : JoinTAddAG Qc := QcJoinTAddAG.

End Stage10.

File "/tmp/tmppwo0hzy0.v", line 241, characters 7-13:
Error: Cannot find module Qcanon