diff --git a/Lebesgue/Set_theory/Set_system/Set_system_base_seq.v b/Lebesgue/Set_theory/Set_system/Set_system_base_seq.v index db6c545b53347bbca2adcee632ab431342ebc62d..c9e466b41e1389a5b0020a429040c5e77c1ca9de 100644 --- a/Lebesgue/Set_theory/Set_system/Set_system_base_seq.v +++ b/Lebesgue/Set_theory/Set_system/Set_system_base_seq.v @@ -377,48 +377,13 @@ rewrite <- trace_union_seq; apply Im, HP, HB. apply union_seq_ext; intros n; symmetry; apply HB. Qed. -(* Is that true? *) -Lemma Trace_Inter_monot_seq : Inter_monot_seq P -> Inter_monot_seq (Trace V P). -Proof. -intros HP A HA1 HA2. -assert (HA3 : forall n, exists B, P B /\ A n = trace V B). - intros n; induction (HA2 n) as [B HB]; exists B; easy. -destruct (choice _ HA3) as [B HB1]. -assert (HB2 : decr_seq B). - intros n. admit. -replace (inter_seq A) with (inter_seq (tracem_seq V B)). -rewrite <- trace_inter_seq; apply Im, HP; try apply HB1; easy. -apply inter_seq_ext; intros n; symmetry; apply HB1. -Admitted. +(* These results are wrong! -(* Is that true? *) +Lemma Trace_Inter_monot_seq : Inter_monot_seq P -> Inter_monot_seq (Trace V P). Lemma Trace_Union_monot_seq : Union_monot_seq P -> Union_monot_seq (Trace V P). -Proof. -intros HP A HA1 HA2. -assert (HA3 : forall n, exists B, P B /\ A n = trace V B). - intros n; induction (HA2 n) as [B HB]; exists B; easy. -destruct (choice _ HA3) as [B HB1]. -assert (HB2 : incr_seq B). - intros n. admit. -replace (union_seq A) with (union_seq (tracem_seq V B)). -rewrite <- trace_union_seq; apply Im, HP; try apply HB1; easy. -apply union_seq_ext; intros n; symmetry; apply HB1. -Admitted. - -(* Is that true? *) Lemma Trace_Union_disj_seq : Union_disj_seq P -> Union_disj_seq (Trace V P). -Proof. -intros HP A HA1 HA2. -assert (HA3 : forall n, exists B, P B /\ A n = trace V B). - intros n; induction (HA2 n) as [B HB]; exists B; easy. -destruct (choice _ HA3) as [B HB1]. -assert (HB2 : disj_seq B). - intros n1 n2 Hn. - admit. -replace (union_seq A) with (union_seq (tracem_seq V B)). -rewrite <- trace_union_seq; apply Im, HP; try apply HB1; easy. -apply union_seq_ext; intros n; symmetry; apply HB1. -Admitted. +Indeed, monotonic or disjoint traces do not imply that the initial sequence is. +Thus, we cannot use the hypothesis... *) End Seq_Facts3. diff --git a/Lebesgue/Set_theory/Set_system/Set_system_seq.v b/Lebesgue/Set_theory/Set_system/Set_system_seq.v index 6b7cb6e8dd0177f03c836b37bc3a17db36bddf99..191d45300df6d462ecaa02fb52afd3a6a9240abe 100644 --- a/Lebesgue/Set_theory/Set_system/Set_system_seq.v +++ b/Lebesgue/Set_theory/Set_system/Set_system_seq.v @@ -1167,20 +1167,9 @@ Context {U : Type}. Variable P : set_system U. Variable V : set U. +(* These results are wrong since unitary results are! Lemma Trace_Monotone_class : is_Monotone_class P -> is_Monotone_class (Trace V P). -Proof. -rewrite 2!Monotone_class_equiv; intros [HP1 HP2]; split; try easy. -apply Trace_Inter_monot_seq; easy. -apply Trace_Union_monot_seq; easy. -Qed. - -Lemma Trace_Lsyst : is_Lsyst P -> is_Lsyst (Trace V P). -Proof. -rewrite 2!Lsyst_equiv; intros [HP1 [HP2 HP3]]; repeat split. -apply Trace_wFull; easy. -apply Trace_Compl; easy. -apply Trace_Union_disj_seq; easy. -Qed. +Lemma Trace_Lsyst : is_Lsyst P -> is_Lsyst (Trace V P). *) Lemma Trace_Sigma_ring : is_Sigma_ring P -> is_Sigma_ring (Trace V P). Proof.