@@ -93,6 +93,9 @@ Import Monoid GRing.Theory BigEnough Order.Theory.
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Local Open Scope ring_scope.
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+ Declare Scope mpoly_scope.
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+ Declare Scope multi_scope.
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+
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Delimit Scope mpoly_scope with MP.
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Delimit Scope multi_scope with MM.
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@@ -159,10 +162,10 @@ Hypothesis ih: forall t1, (forall t2, t2 < t1 -> P t2) -> P t1.
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Lemma ltxwf t : P t.
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Proof .
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- elim: n P ih t => [|k wih] Pn kih t; last case: (tupleP t) => a {t }t.
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+ elim: n P ih t => [|k wih] Pn kih t; last case: (tupleP t) => a {}t.
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by rewrite tuple0; apply/kih=> t2; rewrite tuple0.
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elim/wf: a t => a iha t; elim/wih: t => t iht.
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- apply/kih => t'; case: (tupleP t') => a' {t' }t'; rewrite [_ < _]ltxi_cons.
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+ apply/kih => t'; case: (tupleP t') => a' {}t'; rewrite [_ < _]ltxi_cons.
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by case: (comparableP a a') => //= [/iha/(_ t')|<- /iht].
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Qed .
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@@ -761,7 +764,7 @@ elim/(@ltxwf _ [porderType of nat]): t m=> //=; last first.
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move=> t wih m Em; apply/ih=> m' lt_m'm.
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apply/(wih (tof m'))=> //; rewrite -Em.
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by rewrite /tof ltEsub/= -ltEmnm.
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- move=> Q {ih} ih x; elim: x {-2}x (leqnn x).
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+ move=> Q {} ih x; elim: x {-2}x (leqnn x).
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move=> x; rewrite leqn0=> /eqP->; apply/ih.
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by move=> y; rewrite ltEnat/= ltn0.
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move=> 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.
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case: s => /= [_|m' s srt_s]; first rewrite perm_sym.
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by move/perm_small_eq=> -> //.
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move/perm_mem => <-; rewrite in_cons => /orP[/eqP->//|].
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- elim: s m' srt_s => //= m'' s ih m' /andP[le_mm' /ih {ih }ih].
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+ elim: s m' srt_s => //= m'' s ih m' /andP[le_mm' /ih {}ih].
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by rewrite in_cons => /orP[/eqP->//|] /ih /(le_trans le_mm').
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Qed .
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@@ -4112,7 +4115,7 @@ apply/(irr_sorted_eq (leT := ltn))=> //.
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by apply/ltn_trans.
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by move=> ?; rewrite /ltn /= ltnn.
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move=> m; apply/mapP/mapP; case=> /= x;
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- by rewrite (h, =^~ h)=> {h} h ->; exists x.
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+ by rewrite (h, =^~ h)=> {} h ->; exists x.
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Qed .
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Lemma mesym_tupleE (k : nat) : 's_k =
@@ -4975,7 +4978,7 @@ Lemma homog_prod (s : seq {mpoly R[n]}) :
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Proof .
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move=> homs; apply/homogP; elim: s homs => [_ | p s ihs] /=.
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by exists 0%N; rewrite big_nil; apply/dhomog1.
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- case/andP=> /homogP [dp p_hdp] {ihs }/ihs [d ih].
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+ case/andP=> /homogP [dp p_hdp] {}/ihs [d ih].
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by exists (dp + d)%N; rewrite big_cons; apply/dhomogM.
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Qed .
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