Theorems · Theorem · commutative algebra
seminormFromBounded_aux
∀ {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), 0 ≤ c * f x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CommRingstatement and proof · cited by 17,173
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- le_of_not_gtproof · cited by 430
- mul_nonnegproof · cited by 397
- neg_neg_of_posproof · cited by 227
- div_le_iff₀proof · cited by 97
- one_div_posproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- seminormFromBounded_bddAbove_rangeproof · cited by 5
- seminormFromBounded_leproof · cited by 1