Theorems · Theorem · commutative algebra
seminormFromConst_one
∀ {R : Type u_1} [inst : CommRing R] {c : R} {f : RingSeminorm R},
f 1 ≤ 1 → f c ≠ 0 → IsPowMul ⇑f → seminormFromConst' c f 1 = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 159 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.
Cites10
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 · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- tendsto_const_nhdsproof · cited by 330
- RingSeminormstatement and proof · cited by 58
- IsPowMulstatement and proof · cited by 39
- tendsto_nhds_unique_of_eventuallyEqproof · cited by 13
- seminormFromConst'statement · cited by 13
- tendsto_seminormFromConst_seq_atTopproof · cited by 9
- seminormFromConst_seq_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- seminormFromConst_one_leproof · cited by 0