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nitpick
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affeldt-aist committed Dec 2, 2024
1 parent ff39747 commit 2a6c4a3
Showing 1 changed file with 6 additions and 9 deletions.
15 changes: 6 additions & 9 deletions theories/normedtype.v
Original file line number Diff line number Diff line change
Expand Up @@ -2248,8 +2248,7 @@ split=> [cf|].
- by apply: near_at_right => //; rewrite bnd_simp.
move=> [cf fa]; apply/subspace_continuousP => x /andP[].
rewrite bnd_simp/= le_eqVlt => /predU1P[<-{x}|ax] _.
- apply/cvgrPdist_lt => eps eps_gt0/=.
move/cvgrPdist_lt/(_ _ eps_gt0) : fa.
- apply/cvgrPdist_lt => eps eps_gt0/=; move/cvgrPdist_lt/(_ _ eps_gt0) : fa.
rewrite /at_right !near_withinE; apply: filter_app.
exists 1%R => //= c c1a /[swap]; rewrite in_itv/= andbT le_eqVlt.
by move=> /predU1P[->|/[swap]/[apply]//]; rewrite subrr normr0.
Expand All @@ -2271,13 +2270,11 @@ split=> [cf|].
- by apply: near_at_left => //; rewrite bnd_simp.
move=> [cf fb]; apply/subspace_continuousP => x /andP[_].
rewrite bnd_simp/= le_eqVlt=> /predU1P[->{x}|xb].
- apply/cvgrPdist_lt => eps eps_gt0/=.
move/cvgrPdist_lt/(_ _ eps_gt0) : fb.
rewrite /at_right !near_withinE.
apply: filter_app; exists 1%R => //= c c1b + cb.
rewrite in_itv/= le_eqVlt in cb.
- by case/predU1P : cb => [->|/[swap]/[apply]//]; rewrite subrr normr0.
have xb_i : x \in `]-oo, b[ by rewrite in_itv/=.
- apply/cvgrPdist_lt => eps eps_gt0/=; move/cvgrPdist_lt/(_ _ eps_gt0) : fb.
rewrite /at_right !near_withinE; apply: filter_app.
exists 1%R => //= c c1b /[swap]; rewrite in_itv/= le_eqVlt.
by move=> /predU1P[->|/[swap]/[apply]//]; rewrite subrr normr0.
- have xb_i : x \in `]-oo, b[ by rewrite in_itv/=.
rewrite within_interior; first exact: cf.
suff : `]-oo, b[ `<=` interior `]-oo, b] by exact.
rewrite -open_subsetE; last exact: interval_open.
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