Theorems · Theorem · commutative algebra
seminormFromBounded_nonzero
∀ {R : Type u_1} [inst : CommRing R] {f : R → ℝ} {c : ℝ},
f ≠ 0 → 0 ≤ f → (∀ (x y : R), f (x * y) ≤ c * f x * f y) → seminormFromBounded' f ≠ 0If f : R → ℝ is a nonzero, nonnegative, multiplicatively bounded function, then
seminormFromBounded' f is nonzero.
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- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Pi.zero_applyproof · cited by 70
- Function.ne_iffproof · cited by 40
- seminormFromBounded'statement and proof · cited by 17
- seminormFromBounded_eq_zero_iffproof · cited by 4
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