Theorems · Theorem · functional analysis
norm_sub_norm_le
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), ‖a‖ - ‖b‖ ≤ ‖a - b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_abs_selfproof · cited by 113
- abs_norm_sub_norm_leproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- TendstoLocallyUniformlyOn.inv₀_of_disjointproof · cited by 3
- Asymptotics.IsBigOWith.right_le_sub_of_lt_oneproof · cited by 2
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- ZLattice.summable_norm_sub_rpowproof · cited by 1
- AkraBazziRecurrence.eventually_b_le_rproof · cited by 1
- HasDerivWithinAt.limsup_slope_norm_leproof · cited by 1
- PeriodPair.weierstrassP_boundproof · cited by 1
- Complex.stolzSet_emptyproof · cited by 1
- Complex.norm_one_add_mul_inv_leproof · cited by 1
- ModularForm.exp_isBigO_discriminantproof · cited by 1
- Complex.locally_lipschitz_expproof · cited by 1