diff options
| author | Reynald Affeldt | 2020-05-21 23:32:46 +0900 |
|---|---|---|
| committer | Reynald Affeldt | 2020-05-21 23:32:46 +0900 |
| commit | 83e8892161c8ef3903e302c82a2a7a43f2708d67 (patch) | |
| tree | 3b3fd91bb05e266291f6f9f8a4e7a47563743063 /mathcomp/algebra | |
| parent | 3515b33b1245ea169fbaf61405dc60954509fee2 (diff) | |
three lemmas that we found useful in the context of the
mathcomp-analysis project
Diffstat (limited to 'mathcomp/algebra')
| -rw-r--r-- | mathcomp/algebra/ssralg.v | 3 | ||||
| -rw-r--r-- | mathcomp/algebra/ssrnum.v | 6 |
2 files changed, 9 insertions, 0 deletions
diff --git a/mathcomp/algebra/ssralg.v b/mathcomp/algebra/ssralg.v index 2bde8dd..0e71c86 100644 --- a/mathcomp/algebra/ssralg.v +++ b/mathcomp/algebra/ssralg.v @@ -764,6 +764,9 @@ Proof. by rewrite opprD addrA addrK. Qed. Lemma subrKA z x y : (x - z) + (z + y) = x + y. Proof. by rewrite addrA addrNK. Qed. +Lemma subr_trans z x y : (x - z) + (z - y) = x - y. +Proof. by rewrite addrA addrNK. Qed. + Lemma addr0_eq x y : x + y = 0 -> - x = y. Proof. by rewrite -[-x]addr0 => <-; rewrite addKr. Qed. diff --git a/mathcomp/algebra/ssrnum.v b/mathcomp/algebra/ssrnum.v index e1e5992..41199eb 100644 --- a/mathcomp/algebra/ssrnum.v +++ b/mathcomp/algebra/ssrnum.v @@ -3754,6 +3754,12 @@ Proof. by rewrite lter_norml !lter_sub_addl. Qed. Definition lter_distl := (ler_distl, ltr_distl). +Lemma ltr_distW x y e : `|x - y| < e -> y - e < x. +Proof. by rewrite ltr_distl => /andP[]. Qed. + +Lemma ler_distW x y e : `|x - y| <= e -> y - e <= x. +Proof. by rewrite ler_distl => /andP[]. Qed. + Lemma exprn_even_ge0 n x : ~~ odd n -> 0 <= x ^+ n. Proof. by move=> even_n; rewrite real_exprn_even_ge0 ?num_real. Qed. |