Theorems · Theorem · functional analysis
norm_neg_add
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), ‖-a + b‖ = ‖a - b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- dist_eq_norm_neg_addproof · cited by 46
- dist_eq_norm_subproof · cited by 29
Cited by12
Results whose statement or proof uses this declaration.
- abs_norm_sub_norm_leproof · cited by 7
- lipschitzOnWith_iff_norm_sub_leproof · cited by 3
- uniformCauchySeqOn_ball_of_fderivproof · cited by 2
- tendsto_norm_sub_self_nhdsNEproof · cited by 1
- NormedAddCommGroup.uniformity_basis_distproof · cited by 1
- NormedAddCommGroup.tendsto_nhds_nhdsproof · cited by 1
- controlled_closure_of_completeproof · cited by 1
- difference_quotients_converge_uniformlyproof · cited by 1
- OrthogonalFamily.summable_iff_norm_sq_summableproof · cited by 1
- uniformCauchySeqOnFilter_of_fderivproof · cited by 1
- NormedAddCommGroup.nhds_basis_norm_ltproof · cited by 0
- ball_eqproof · cited by 0