@@ -93,6 +93,9 @@ Import Monoid GRing.Theory BigEnough Order.Theory.
9393
9494Local Open Scope ring_scope.
9595
96+ Declare Scope mpoly_scope.
97+ Declare Scope multi_scope.
98+
9699Delimit Scope mpoly_scope with MP.
97100Delimit Scope multi_scope with MM.
98101
@@ -159,10 +162,10 @@ Hypothesis ih: forall t1, (forall t2, t2 < t1 -> P t2) -> P t1.
159162
160163Lemma ltxwf t : P t.
161164Proof .
162- elim: n P ih t => [|k wih] Pn kih t; last case: (tupleP t) => a {t }t.
165+ elim: n P ih t => [|k wih] Pn kih t; last case: (tupleP t) => a {}t.
163166 by rewrite tuple0; apply/kih=> t2; rewrite tuple0.
164167elim/wf: a t => a iha t; elim/wih: t => t iht.
165- apply/kih => t'; case: (tupleP t') => a' {t' }t'; rewrite [_ < _]ltxi_cons.
168+ apply/kih => t'; case: (tupleP t') => a' {}t'; rewrite [_ < _]ltxi_cons.
166169by case: (comparableP a a') => //= [/iha/(_ t')|<- /iht].
167170Qed .
168171
@@ -761,7 +764,7 @@ elim/(@ltxwf _ [porderType of nat]): t m=> //=; last first.
761764 move=> t wih m Em; apply/ih=> m' lt_m'm.
762765 apply/(wih (tof m'))=> //; rewrite -Em.
763766 by rewrite /tof ltEsub/= -ltEmnm.
764- move=> Q {ih} ih x; elim: x {-2}x (leqnn x).
767+ move=> Q {} ih x; elim: x {-2}x (leqnn x).
765768 move=> x; rewrite leqn0=> /eqP->; apply/ih.
766769 by move=> y; rewrite ltEnat/= ltn0.
767770move=> k wih l le_l_Sk; apply/ih=> y; rewrite ltEnat => lt_yl.
@@ -2420,7 +2423,7 @@ have: sorted <=%O%O s by apply/sort_sorted/le_total.
24202423case: s => /= [_|m' s srt_s]; first rewrite perm_sym.
24212424 by move/perm_small_eq=> -> //.
24222425move/perm_mem => <-; rewrite in_cons => /orP[/eqP->//|].
2423- elim: s m' srt_s => //= m'' s ih m' /andP[le_mm' /ih {ih }ih].
2426+ elim: s m' srt_s => //= m'' s ih m' /andP[le_mm' /ih {}ih].
24242427by rewrite in_cons => /orP[/eqP->//|] /ih /(le_trans le_mm').
24252428Qed .
24262429
@@ -4112,7 +4115,7 @@ apply/(irr_sorted_eq (leT := ltn))=> //.
41124115 by apply/ltn_trans.
41134116 by move=> ?; rewrite /ltn /= ltnn.
41144117move=> m; apply/mapP/mapP; case=> /= x;
4115- by rewrite (h, =^~ h)=> {h} h ->; exists x.
4118+ by rewrite (h, =^~ h)=> {} h ->; exists x.
41164119Qed .
41174120
41184121Lemma mesym_tupleE (k : nat) : 's_k =
@@ -4975,7 +4978,7 @@ Lemma homog_prod (s : seq {mpoly R[n]}) :
49754978Proof .
49764979move=> homs; apply/homogP; elim: s homs => [_ | p s ihs] /=.
49774980 by exists 0%N; rewrite big_nil; apply/dhomog1.
4978- case/andP=> /homogP [dp p_hdp] {ihs }/ihs [d ih].
4981+ case/andP=> /homogP [dp p_hdp] {}/ihs [d ih].
49794982by exists (dp + d)%N; rewrite big_cons; apply/dhomogM.
49804983Qed .
49814984
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