Theorems · Theorem · commutative algebra

IsDiscreteValuationRing.bot_lt_toWithBotNat_iff

∀ {R : Type u_2} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] (x : R),
  ⊥ < IsDiscreteValuationRing.toWithBotNat x ↔ x ≠ 0

Defined in: Mathlib.RingTheory.DiscreteValuationRing.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain IsDiscreteValuationRing

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CommRingstatement and proof · cited by 17,173
Bot.botstatement · cited by 4,720
IsDomainstatement and proof · cited by 2,196
WithBotstatement · cited by 1,498
IsDiscreteValuationRingstatement and proof · cited by 117
bot_lt_iff_ne_botproof · cited by 57
IsDiscreteValuationRing.toWithBotNatstatement · cited by 6

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