Theorems · Theorem · functional analysis
nnnorm_mul_le_of_le
∀ {α : Type u_2} [inst : NonUnitalSeminormedRing α] {a₁ a₂ : α} {r₁ r₂ : NNReal},
‖a₁‖₊ ≤ r₁ → ‖a₂‖₊ ≤ r₂ → ‖a₁ * a₂‖₊ ≤ r₁ * r₂- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalSeminormedRing
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.
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- NNNorm.nnnormstatement and proof · cited by 952
- mul_le_mul'proof · cited by 274
- NonUnitalSeminormedRingstatement and proof · cited by 44
- nnnorm_mul_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_mul₃_leproof · cited by 0