Theorems · Theorem · commutative algebra
seminormFromConst_seq_antitone
∀ {R : Type u_1} [inst : CommRing R] {c : R} {f : RingSeminorm R},
f 1 ≤ 1 → f c ≠ 0 → IsPowMul ⇑f → ∀ (x : R), Antitone (seminormFromConst_seq c f x)seminormFromConst_seq c f x is antitone.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 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.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- le_transproof · cited by 985
- div_eq_mul_invproof · cited by 715
- Antitonestatement · cited by 563
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_seminormFromConst_seq_atTopproof · cited by 9