Theorems · Theorem · functional analysis
norm_mul_le_of_le
∀ {α : Type u_2} [inst : NonUnitalSeminormedRing α] {a₁ a₂ : α} {r₁ r₂ : ℝ}, ‖a₁‖ ≤ r₁ → ‖a₂‖ ≤ r₂ → ‖a₁ * a₂‖ ≤ r₁ * r₂- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 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.
Cites7
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
- LE.le.transproof · cited by 3,151
- norm_nonnegproof · cited by 725
- mul_le_mulproof · cited by 144
- NonUnitalSeminormedRingstatement and proof · cited by 44
- norm_mul_leproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- norm_mul₃_leproof · cited by 1