diff --git a/.github/workflows/docker-action.yml b/.github/workflows/docker-action.yml
index 349b22a..f86dbb6 100644
--- a/.github/workflows/docker-action.yml
+++ b/.github/workflows/docker-action.yml
@@ -1,5 +1,3 @@
-# This file was generated from `meta.yml`, please do not edit manually.
-# Follow the instructions on https://github.com/coq-community/templates to regenerate.
 name: Docker CI
 
 on:
@@ -24,7 +22,7 @@ jobs:
           - 'mathcomp/mathcomp:2.0.0-coq-8.16'
       fail-fast: false
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: coq-community/docker-coq-action@v1
         with:
           custom_image: ${{ matrix.image }}
diff --git a/README.md b/README.md
index f82334b..91cdbf8 100644
--- a/README.md
+++ b/README.md
@@ -36,9 +36,9 @@ and number theory.
 - Coq-community maintainer(s):
   - Laurent Théry ([**@thery**](https://github.com/thery))
 - License: [MIT License](LICENSE)
-- Compatible Coq versions: 8.10 or later
+- Compatible Coq versions: 8.16 or later
 - Additional dependencies:
-  - [MathComp ssreflect 1.12 or later](https://math-comp.github.io)
+  - [MathComp ssreflect 2.0 or later](https://math-comp.github.io)
   - [MathComp algebra](https://math-comp.github.io)
 - Coq namespace: `gaia`
 - Related publication(s):
diff --git a/coq-gaia-numbers.opam b/coq-gaia-numbers.opam
index 306ea70..51268dd 100644
--- a/coq-gaia-numbers.opam
+++ b/coq-gaia-numbers.opam
@@ -14,9 +14,9 @@ Elements of Mathematics in Coq using the Mathematical Components library."""
 
 build: ["dune" "build" "-p" name "-j" jobs]
 depends: [
-  "dune" {>= "2.5"}
-  "coq" {(>= "8.16" & < "8.18~") | (= "dev")}
-  "coq-mathcomp-ssreflect" {(>= "2.0.0" & < "2.1~") | (= "dev")}
+  "dune" {>= "2.8"}
+  "coq" {>= "8.16"}
+  "coq-mathcomp-ssreflect" {>= "2.0"}
   "coq-mathcomp-algebra"
   "coq-gaia-theory-of-sets" {= version}
   "coq-gaia-ordinals" {= version}
diff --git a/coq-gaia-ordinals.opam b/coq-gaia-ordinals.opam
index bc16249..2b8201f 100644
--- a/coq-gaia-ordinals.opam
+++ b/coq-gaia-ordinals.opam
@@ -14,9 +14,9 @@ the Mathematical Components library."""
 
 build: ["dune" "build" "-p" name "-j" jobs]
 depends: [
-  "dune" {>= "2.5"}
-  "coq" {(>= "8.16" & < "8.18~") | (= "dev")}
-  "coq-mathcomp-ssreflect" {(>= "2.0.0" & < "2.1~") | (= "dev")}
+  "dune" {>= "2.8"}
+  "coq" {>= "8.16"}
+  "coq-mathcomp-ssreflect" {>= "2.0"}
   "coq-gaia-theory-of-sets" {= version}
   "coq-gaia-schutte" {= version}
 ]
diff --git a/coq-gaia-schutte.opam b/coq-gaia-schutte.opam
index e24f573..88ebc44 100644
--- a/coq-gaia-schutte.opam
+++ b/coq-gaia-schutte.opam
@@ -14,9 +14,9 @@ following the approaches of Schütte and Ackermann."""
 
 build: ["dune" "build" "-p" name "-j" jobs]
 depends: [
-  "dune" {>= "2.5"}
-  "coq" {(>= "8.16" & < "8.18~") | (= "dev")}
-  "coq-mathcomp-ssreflect" {(>= "2.0.0" & < "2.1~") | (= "dev")}
+  "dune" {>= "2.8"}
+  "coq" {>= "8.16"}
+  "coq-mathcomp-ssreflect" {>= "2.0"}
 ]
 
 tags: [
diff --git a/coq-gaia-stern.opam b/coq-gaia-stern.opam
index 8e92e37..c932dd3 100644
--- a/coq-gaia-stern.opam
+++ b/coq-gaia-stern.opam
@@ -14,9 +14,9 @@ Mathematical Components library."""
 
 build: ["dune" "build" "-p" name "-j" jobs]
 depends: [
-  "dune" {>= "2.5"}
-  "coq" {(>= "8.16" & < "8.18~") | (= "dev")}
-  "coq-mathcomp-ssreflect" {(>= "2.0.0" & < "2.1~") | (= "dev")}
+  "dune" {>= "2.8"}
+  "coq" {>= "8.16"}
+  "coq-mathcomp-ssreflect" {>= "2.0"}
   "coq-mathcomp-algebra"
 ]
 
diff --git a/coq-gaia-theory-of-sets.opam b/coq-gaia-theory-of-sets.opam
index 9f52134..326b581 100644
--- a/coq-gaia-theory-of-sets.opam
+++ b/coq-gaia-theory-of-sets.opam
@@ -14,9 +14,9 @@ Elements of Mathematics in Coq using the Mathematical Components library."""
 
 build: ["dune" "build" "-p" name "-j" jobs]
 depends: [
-  "dune" {>= "2.5"}
-  "coq" {(>= "8.16" & < "8.18~") | (= "dev")}
-  "coq-mathcomp-ssreflect" {(>= "2.0.0" & < "2.1~") | (= "dev")}
+  "dune" {>= "2.8"}
+  "coq" {>= "8.16"}
+  "coq-mathcomp-ssreflect" {>= "2.0"}
 ]
 
 tags: [
diff --git a/dune-project b/dune-project
index 62cddbe..b887d64 100644
--- a/dune-project
+++ b/dune-project
@@ -1,3 +1,3 @@
-(lang dune 2.5)
-(using coq 0.2)
+(lang dune 2.8)
+(using coq 0.3)
 (name gaia)
diff --git a/meta.yml b/meta.yml
index c6ea4ee..46948a5 100644
--- a/meta.yml
+++ b/meta.yml
@@ -61,15 +61,15 @@ license:
   identifier: MIT
 
 supported_coq_versions:
-  text: '8.10 or later'
-  opam: '{(>= "8.10" & < "8.17~") | (= "dev")}'
+  text: '8.16 or later'
+  opam: '{>= "8.16"}'
 
 dependencies:
 - opam:
     name: coq-mathcomp-ssreflect
-    version: '{(>= "1.12.0" & < "1.16~") | (= "dev")}'
+    version: '{>= "2.0"}'
   description: |-
-    [MathComp ssreflect 1.12 or later](https://math-comp.github.io)
+    [MathComp ssreflect 2.0 or later](https://math-comp.github.io)
 - opam:
     name: coq-mathcomp-algebra
   description: |-
@@ -78,41 +78,13 @@ dependencies:
 tested_coq_opam_versions:
 - version: 'coq-dev'
   repo: 'mathcomp/mathcomp-dev'
-- version: 'coq-8.16'
-  repo: 'mathcomp/mathcomp-dev'
-- version: 'coq-8.15'
+- version: 'coq-8.17'
   repo: 'mathcomp/mathcomp-dev'
-- version: 'coq-8.14'
-  repo: 'mathcomp/mathcomp-dev'
-- version: 'coq-8.13'
+- version: 'coq-8.16'
   repo: 'mathcomp/mathcomp-dev'
-- version: '1.15.0-coq-8.16'
-  repo: 'mathcomp/mathcomp'
-- version: '1.15.0-coq-8.15'
-  repo: 'mathcomp/mathcomp'
-- version: '1.15.0-coq-8.14'
-  repo: 'mathcomp/mathcomp'
-- version: '1.14.0-coq-8.15'
-  repo: 'mathcomp/mathcomp'
-- version: '1.14.0-coq-8.14'
-  repo: 'mathcomp/mathcomp'
-- version: '1.13.0-coq-8.14'
-  repo: 'mathcomp/mathcomp'
-- version: '1.13.0-coq-8.13'
-  repo: 'mathcomp/mathcomp'
-- version: '1.13.0-coq-8.12'
-  repo: 'mathcomp/mathcomp'
-- version: '1.13.0-coq-8.11'
-  repo: 'mathcomp/mathcomp'
-- version: '1.12.0-coq-8.14'
-  repo: 'mathcomp/mathcomp'
-- version: '1.12.0-coq-8.13'
-  repo: 'mathcomp/mathcomp'
-- version: '1.12.0-coq-8.12'
-  repo: 'mathcomp/mathcomp'
-- version: '1.12.0-coq-8.11'
+- version: '2.0.0-coq-8.17'
   repo: 'mathcomp/mathcomp'
-- version: '1.12.0-coq-8.10'
+- version: '2.0.0-coq-8.16'
   repo: 'mathcomp/mathcomp'
 
 namespace: gaia
diff --git a/theories/sets/sset2_aux.v b/theories/sets/sset2_aux.v
index b419031..b3017c5 100644
--- a/theories/sets/sset2_aux.v
+++ b/theories/sets/sset2_aux.v
@@ -745,7 +745,7 @@ case: (emptyset_dichot c) => hyp.
   have [pa pb pc]:= empty_function_function.
   rewrite ae in pb; rewrite hyp in pc.
   exists (bcreate pa pb pc) => v.
-  elimtype False; rewrite -ae in v; case: v.
+  exfalso; rewrite -ae in v; case: v.
 have [x [xc _]]:= hyp.
 move: (exists_left_inv_from_injC (inhabits xc) ig) => [r rv].
 exists (r \o f). 
diff --git a/theories/sets/ssete1.v b/theories/sets/ssete1.v
index dedacea..a8808a6 100644
--- a/theories/sets/ssete1.v
+++ b/theories/sets/ssete1.v
@@ -1681,7 +1681,7 @@ have sh: surjection h.
   by ex_tac; rewrite /hz; aw; rewrite Y_false. 
 have WWh: forall x, inc x Ea -> Vf f (hz x) = Vf (canon_proj r) (P x).
   move=> x xEa.
-  have xE: inc x E by rewrite /E; aw; intuition.
+  have xE: inc x E by rewrite /E; aw; intuition auto with fprops.
   have Ps: inc (P x) (substrate r) by rewrite - sr -gzP//; apply: gzp'.
   rewrite /hz canon_proj_V//.
   move /setX_P: xEa=> [px PF] /set1_P ->; Ytac0.
diff --git a/theories/stern/fibm.v b/theories/stern/fibm.v
index dddf973..56d9c95 100644
--- a/theories/stern/fibm.v
+++ b/theories/stern/fibm.v
@@ -2087,10 +2087,10 @@ have: x *+ 2  = z + (y+1) by rewrite /z subrK.
 have h u: (u.*2)%:Z = (u%:Z) *+ 2 by rewrite -muln2 PoszM - mulr_natr.
 case: eq3 => ->; rewrite hb eq1 ha - PoszD fib_doubleS mulnC.
   rewrite  - addnA (addnA (fib n.*2 ^ 2)%N) -(DE1_sol n).
-  by move/eqP;rewrite addnn h eqr_muln2r /= => /eqP; left.
+  by move/eqP;rewrite addnn h eqrMn2r /= => /eqP; left.
 move => hw; right; apply/eqP;move: (DE1_sol n) hw.
 rewrite -[X in _ *+2 = X] opprK opprD opprK - addnA addn1 => ->.
-by move/eqP; rewrite addnAC addnn PoszD addrK h -mulNrn eqr_muln2r.
+by move/eqP; rewrite addnAC addnn PoszD addrK h -mulNrn eqrMn2r.
 Qed.
 
 Lemma DE_eq6_neg x y: y <0 -> DE_eq6 x y -> 
@@ -2115,10 +2115,10 @@ have h u: (u.*2)%:Z = (u%:Z) *+ 2 by rewrite -muln2 PoszM - mulr_natr.
 have: x *+ 2  = z +1 + (-(-y)) by rewrite opprK addrAC -addrA /z subrK.
 case: eq4 => ->; rewrite hb -doubleS fib_doubleS eq1 ha.
   rewrite - (PoszD _ 1%N) addnAC (DE2_sol n) addnAC PoszD addrK addnn.
-  by move/eqP; rewrite h eqr_muln2r /= => /eqP; left.
+  by move/eqP; rewrite h eqrMn2r /= => /eqP; left.
 move => hw; right; apply/eqP; move /eqP: hw.
 rewrite addrAC -opprD - PoszD - addnA -(DE2_sol n) addnA addnn PoszD opprD.
-by rewrite addrK h -mulNrn eqr_muln2r.
+by rewrite addrK h -mulNrn eqrMn2r.
 Qed.
 
 
diff --git a/theories/stern/stern.v b/theories/stern/stern.v
index 3135daf..2ea9b99 100644
--- a/theories/stern/stern.v
+++ b/theories/stern/stern.v
@@ -801,7 +801,7 @@ Proof. by have [-> // | d_nz] := altP eqP; rewrite -{1}[d]mul1r mulzK. Qed.
 Lemma ltz_pmod m d : d > 0 -> (m %% d)%Z < d.
 Proof.
 case: m d => n [] // d d_gt0; first by rewrite modz_nat ltz_nat ltn_pmod.
-by rewrite modNz_nat // -lez_addr1 addrAC subrK ger_addl oppr_le0.
+by rewrite modNz_nat // -lezD1 addrAC subrK gerDl oppr_le0.
 Qed.
 
 
@@ -814,7 +814,7 @@ case: p => // p p_gt0; wlog d_gt0: d / d > 0; last case: d => // d in d_gt0 *.
   by move=> IH; case/intP: d => [|d|d]; rewrite ?mulr0 ?divz0 ?mulrN ?divzN ?IH.
 rewrite {1}(divz_eq m d) mulrDr mulrCA divzMDl ?mulf_neq0 ?Order.POrderTheory.gt_eqF // addrC.
 rewrite divz_small ?add0r // PoszM pmulr_rge0 ?modz_ge0 ?Order.POrderTheory.gt_eqF //=.
-by rewrite ltr_pmul2l ?ltz_pmod.
+by rewrite ltr_pM2l ?ltz_pmod.
 Qed.
 
 
@@ -837,15 +837,15 @@ Qed.
  
 Lemma ltz_ceil m d : d > 0 -> m < ((m %/ d)%Z + 1) * d.
 Proof.
-by case: d => // d d_gt0; rewrite mulrDl mul1r -ltr_subl_addl ltz_mod ?Order.POrderTheory.gt_eqF.
+by case: d => // d d_gt0; rewrite mulrDl mul1r -ltrBlDl ltz_mod ?Order.POrderTheory.gt_eqF.
 Qed.
 
 Lemma ltz_divLR m n d : d > 0 -> ((m %/ d)%Z < n) = (m < n * d).
 Proof.
 move=> d_gt0; apply/idP/idP.
-  rewrite -(lez_addr1 _ n) -(ler_pmul2r d_gt0).
+  rewrite -(lezD1 _ n) -(ler_pM2r d_gt0).
   exact: (Order.POrderTheory.lt_le_trans (ltz_ceil _ _)).
-rewrite -(ltr_pmul2r d_gt0 _ n) //; apply: Order.POrderTheory.le_lt_trans (lez_floor _ _).
+rewrite -(ltr_pM2r d_gt0 _ n) //; apply: Order.POrderTheory.le_lt_trans (lez_floor _ _).
 by rewrite Order.POrderTheory.gt_eqF.
 Qed.
 
@@ -891,7 +891,7 @@ Proof. by rewrite rmorphD. Qed.
 Lemma floorp1 x (y:= (floorq x)%:Q): y <= x < y+1.
 Proof.
 have ha: 0 < (denq x)%:Q by rewrite  ltr0z (denq_gt0 x).
-rewrite -(divq_num_den x) ler_pdivl_mulr // succq  ltr_pdivr_mulr //.
+rewrite -(divq_num_den x) ler_pdivlMr // succq  ltr_pdivrMr //.
 rewrite - !rmorphM /= ler_int ltr_int lez_floor // ltz_ceil //.
 Qed.
 
@@ -899,14 +899,14 @@ Qed.
 Lemma floorp2 x (y: int): y%:Q <= x < y%:Q +1 ->  y = floorq x.
 Proof.
 move: (floorp1 x) => /andP [sa sb] /andP [sc sd].
-apply/eqP;  rewrite Order.POrderTheory.eq_le - !ltz_addr1 -! (ltr_int rat).
+apply/eqP;  rewrite Order.POrderTheory.eq_le - !ltzD1 -! (ltr_int rat).
 by rewrite - !succq (Order.POrderTheory.le_lt_trans sc sb) (Order.POrderTheory.le_lt_trans sa sd).
 Qed.
 
 Lemma floor_ge0 x: 0 <= x -> 0 <= floorq x.
 Proof.
 move /andP:(floorp1 x) => [la lb] lc. 
-by move: (Order.POrderTheory.le_lt_trans lc lb); rewrite  succq ltr0z ltz_addr1.
+by move: (Order.POrderTheory.le_lt_trans lc lb); rewrite  succq ltr0z ltzD1.
 Qed.
 
 Lemma floor_small x: 0 <= x < 1 -> floorq x = 0.
@@ -921,7 +921,7 @@ Qed.
 Lemma floor_sum (a:rat) (b: int):  floorq (a + b%:Q) = floorq a + b.
 Proof.
 symmetry; apply:floorp2; case/andP:(floorp1 a) => [l1 l2].
-by rewrite intrD ler_add2r l1 addrAC ltr_add2r l2.
+by rewrite intrD lerD2r l1 addrAC ltrD2r l2.
 Qed.
 
 
@@ -987,7 +987,7 @@ Lemma Sn_1: Sn 1 = 1/(2%:Q).  Proof. by []. Qed.
 Lemma Sn_gt0 x: 0 <= x -> 0 < Sn x.
 Proof.
 rewrite /Sn doubleq addrA  (addrC (1 + _)) -addrA => h.
-rewrite invr_gt0 -(addr0 0); apply:ler_lt_add;first by rewrite ler0z floor_ge0.
+rewrite invr_gt0 -(addr0 0); apply:ler_ltD;first by rewrite ler0z floor_ge0.
 by rewrite subr_gt0 addrC; case /andP:(floorp1 x) => [_].
 Qed.
 
@@ -1025,12 +1025,12 @@ Qed.
 Lemma Sn_lt1 (a b: int)  (A := a%:Q) (B := b%:Q):
   0 <= a -> 0 < b  -> Sn (A / (A + B)) = (A + B) / B.
 Proof.
-move => la lb; move: (ler_lt_add la lb); rewrite addr0 => lab.
+move => la lb; move: (ler_ltD la lb); rewrite addr0 => lab.
 have labq:  0 < (a + b)%:Q by rewrite ltr0z.
 have dnz: (a + b)%:Q != 0 by move: labq; rewrite lt0r => /andP [].
 have ha: 0 <= a%:Q / (a + b)%:Q < 1.
-  rewrite divr_ge0 ?ler0z ? (ltrW lab)//= ?ltr_pdivr_mulr //.
-    by rewrite mul1r ltr_int - {1} (addr0  a) ltr_add2l.
+  rewrite divr_ge0 ?ler0z ? (ltrW lab)//= ?ltr_pdivrMr //.
+    by rewrite mul1r ltr_int - {1} (addr0  a) ltrD2l.
   by move: lab; rewrite lt0r; move/andP => [la1 la2].
 rewrite Sn_small - intrD // -(invf_div b%:~R) subf_div1 //.
 by rewrite - rmorphB /= {1} (addrC a) - addrA subrr addr0.
@@ -1075,7 +1075,7 @@ Qed.
 
 Lemma SCF_pos2 a L : all (fun z => 0 < z) L ->  a <= SCF (a::L).
 Proof.
-rewrite /SCF - {1}(addr0 a) ler_add2l.
+rewrite /SCF - {1}(addr0 a) lerD2l.
 case lz: (L== nil) => h; first by rewrite (eqP lz).
 by rewrite Order.POrderTheory.ltW ?  SCF_pos1 ? lz //=.
 Qed.
@@ -1229,7 +1229,7 @@ Lemma CF_bound a l: good_for_cf a l -> floorq a = floorq (SCF (a::l)).
 Proof.
 move => /and3P [ha hb hc]. 
 have ap:= (all_rat_in_P_pos hb).
-apply: floorp2;rewrite -(eqP ha)(SCF_pos2 _ ap) /= ltr_add2l.
+apply: floorp2;rewrite -(eqP ha)(SCF_pos2 _ ap) /= ltrD2l.
 move: hb hc ap; case:l => // c l hb hc /= /andP[_ ap]. 
 suff ww: 1 < c + SCF' l by rewrite /= div1r invf_lt1 // (Order.POrderTheory.lt_trans ltr01 ww).
 move: hb => /= /andP [/rat_in_P_ge1 cp hb].
@@ -1237,7 +1237,7 @@ case lz: (l== [::]).
   move:hc lz cp; clear;case: l => //= ca _ cb. 
   by rewrite addr0 Order.POrderTheory.lt_neqAle eq_sym ca cb.
 have la: 0 <  SCF' l by apply:SCF_pos1 =>//; rewrite lz. 
-by move:(ler_lt_add cp la); rewrite addr0.
+by move:(ler_ltD cp la); rewrite addr0.
 Qed.
 
 
@@ -1282,7 +1282,7 @@ move: (absz_denq x); set b := absz _; set a := absz _ => bv av.
 have bp: (0 < b)%N by move: (denq_gt0 x); rewrite - bv; case: (b).
 move: (divq_num_den x); rewrite - bv - av => xv.
 case: (posnP a) => ap; first by move: xp; rewrite - xv ap mul0r. 
-have: x * b%:~R < b%:~R by rewrite gtr_pmull // ltr0n.
+have: x * b%:~R < b%:~R by rewrite gtr_pMl // ltr0n.
 rewrite bv - (numqE x) - bv - av ltr_int ltz_nat - xv => lab.
 move: ap lab; move: (leqnn b); clear; move:a b {-2} (b) => a n b {x}.
 elim: n a b. 
@@ -1313,7 +1313,7 @@ Lemma CF_exists (x: rat):  exists a l, good_for_cf a l /\ x = SCF (a::l).
 Proof.
 move: (floorp1 x) => /=; set a := (floorq x)%:~R => /andP[eq1 eq2].
 have ra:  rat_in_Z a by apply: rat_in_Z_int.
-have: 0 <= x - a < 1 by rewrite subr_ge0 eq1 ltr_subl_addr addrC eq2.
+have: 0 <= x - a < 1 by rewrite subr_ge0 eq1 ltrBlDr addrC eq2.
 rewrite Order.POrderTheory.le_eqVlt eq_sym subr_eq0.
 case:eqP => xa /=.
   by move => _; exists a, [::]; rewrite /= addr0 /good_for_cf ra.
@@ -1398,7 +1398,7 @@ case => [// | a  [ // | b l]].
 rewrite continuantS ltnS -/(size _) => /ltnW sLn /andP [sa sb].
 move/andP: (sb); rewrite [odd _]/= negbK => [][_ sc] os.
 have: 0 <= a * K (b :: l) by apply: (mulr_ge0 sa); apply:continuant_ge0. 
-by rewrite - (ler_addr (K l));apply: Order.POrderTheory.lt_le_trans; apply:IH.
+by rewrite - (lerDr (K l));apply: Order.POrderTheory.lt_le_trans; apply:IH.
 Qed.
 
 Lemma continuant_zeroA l: odd (size l) ->
@@ -1914,7 +1914,7 @@ Proof. by rewrite /Sba_m /Sba_j invrK /Sba_i. Qed.
 
 
 Lemma Sba_p_pos x: 0 < x -> 1 < (Sba_p x).
-Proof. by move => h; rewrite /Sba_p -ltr_subl_addl. Qed.
+Proof. by move => h; rewrite /Sba_p -ltrBlDl. Qed.
 
 Lemma Sba_m_pos x: 1 < x -> 0 < (Sba_m x).
 Proof. by move => h; rewrite /Sba_m subr_gt0.  Qed.
@@ -1962,7 +1962,7 @@ Proof.
 move => xp; apply /negP => h.
 move: (snumden_pos (Order.POrderTheory.ltW xp)); rewrite (eqP h) /snumden' => eq1.
 move:xp (denq_gt0 x); rewrite - numq_gt0 ! gtz0_ge1 => sa sb.
-by move: (ler_add sa sb); rewrite eq1. 
+by move: (lerD sa sb); rewrite eq1. 
 Qed.
 
 Lemma snumden_inv x:  0 < x  -> snumden x = snumden (x^-1).
@@ -1984,7 +1984,7 @@ case/ratP: (x-1) => n d cp n0.
 have H: coprime `|n + d.+1| d.+1.
   by rewrite - (gtz0_abs n0) - PoszD /= /coprime gcdnC gcdnDr gcdnC.
 rewrite (addrC _ 1) addf_div1 ?intr_eq0 //- intrD coprimeq_den //.
-by rewrite coprimeq_num // sgrEz /= gtr0_sgz // mul1r ltr_addl normr_gt0.
+by rewrite coprimeq_num // sgrEz /= gtr0_sgz // mul1r ltrDl normr_gt0.
 Qed.