Theorems · Theorem · functional analysis
enorm_add_le_of_le
∀ {E : Type u_8} [inst : TopologicalSpace E] [inst_1 : ESeminormedAddMonoid E] {r₁ r₂ : ENNReal} {a₁ a₂ : E},
‖a₁‖ₑ ≤ r₁ → ‖a₂‖ₑ ≤ r₂ → ‖a₁ + a₂‖ₑ ≤ r₁ + r₂- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement and proof · cited by 9,879
- LE.le.transproof · cited by 3,151
- ENorm.enormstatement and proof · cited by 715
- add_le_addproof · cited by 666
- ESeminormedAddMonoidstatement and proof · cited by 133
- enorm_add_leproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- enorm_add₃_leproof · cited by 1
- enorm_add₄_leproof · cited by 1