Theorems · Theorem · commutative algebra
seminormFromBounded_ge
∀ {R : Type u_1} [inst : CommRing R] {f : R → ℝ} {c : ℝ},
0 ≤ f → (∀ (x y : R), f (x * y) ≤ c * f x * f y) → ∀ (x : R), f x ≤ f 1 * seminormFromBounded' f xIf f : R → ℝ is a nonnegative, multiplicatively bounded function, then for every x : R,
f x ≤ f 1 * seminormFromBounded' f x.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- div_le_iff₀proof · cited by 97
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- seminormFromBounded'statement and proof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- seminormFromBounded_eq_zero_iffproof · cited by 4