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Merged
CohenCyril merged 1 commit into from
Jan 13, 2021
Merged

Get rid of ssrnum.mc_1_10 #319

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11 changes: 5 additions & 6 deletions theories/sequences.v
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,6 @@ Require Import classical_sets posnum topology normedtype landau derive forms.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Import mc_1_10.Num.Theory. (* because 1.11.0+beta1 does have bugs! *)
Import Order.TTheory GRing.Theory Num.Def Num.Theory.

Local Open Scope classical_set_scope.
Expand Down Expand Up @@ -103,15 +102,15 @@ Proof. by apply: homo_leq (fun _ _ _ u v => le_trans v u). Qed.

Lemma increasing_seqP (T : numDomainType) (u_ : T ^nat) :
(forall n, u_ n < u_ n.+1) -> increasing_seq u_.
Proof. by move=> u_nondec; apply: lenr_mono; apply: homo_ltn lt_trans _. Qed.
Proof. by move=> u_nondec; apply: le_mono; apply: homo_ltn lt_trans _. Qed.

Lemma decreasing_seqP (T : numDomainType) (u_ : T ^nat) :
(forall n, u_ n > u_ n.+1) -> decreasing_seq u_.
Proof.
move=> u_noninc;
(* FIXME: add shortcut to order.v *)
apply: (@total_homo_mono _ _ _ leq ltn ger gtr leqnn (@lerr _)
ltn_neqAle _ (fun _ _ _ => esym (ler_anti _)) leq_total
apply: (@total_homo_mono _ _ _ leq ltn ger gtr leqnn lexx
ltn_neqAle _ (fun _ _ _ => esym (le_anti _)) leq_total
(homo_ltn (fun _ _ _ u v => lt_trans v u) _)) => //.
by move=> x y; rewrite /= lt_neqAle eq_sym.
Qed.
Expand Down Expand Up @@ -420,7 +419,7 @@ have [p /andP[M0u_p u_pM0]] : exists p, M0 - e%:num <= u_ p <= M0.
exists p; rewrite M0u_p /=; have /ubP := sup_upper_bound supS.
by apply; exists p.
near=> n; have pn : (p <= n)%N by near: n; apply: nbhs_infty_ge.
rewrite distrC ler_norml ler_sub_addl (ler_trans M0u_p (u_nd _ _ pn)) /=.
rewrite distrC ler_norml ler_sub_addl (le_trans M0u_p (u_nd _ _ pn)) /=.
rewrite ler_subl_addr (@le_trans _ _ M0) ?ler_addr //.
by have /ubP := sup_upper_bound supS; apply; exists n.
Grab Existential Variables. all: end_near. Qed.
Expand Down Expand Up @@ -949,7 +948,7 @@ have [re1|re1] := ltrP (`|contract l - e%:num|) 1; last first.
by rewrite subr_le0 (le_trans (ltW l0)).
rewrite opprB ler_subr_addr addrC -ler_subr_addr in re1.
rewrite ltr_subl_addr (le_lt_trans re1) // -ltr_subl_addl addrAC subrr add0r.
rewrite ltr_neqAle eq_sym contract_eqN1 unoo /=.
rewrite lt_neqAle eq_sym contract_eqN1 unoo /=.
by case/ler_normlP : (contract_le1 (u_ n)); rewrite ler_oppl.
pose e' := r - real_of_er (expand (contract l - e%:num)).
have e'0 : 0 < e'.
Expand Down