Theorems · Theorem · field theory
Valued.integer.isPrincipalIdealRing_of_compactSpace
∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
[hc : CompactSpace ↥(Valued.integer K)], IsPrincipalIdealRing ↥(Valued.integer K)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Unitsproof · cited by 2,804
- IsCompactproof · cited by 1,282
- LocallyFiniteOrderproof · cited by 658
- Subringstatement · cited by 602
- CompactSpacestatement and proof · cited by 593
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- DenselyOrderedproof · cited by 471
- Valued.vproof · cited by 163
- IsPrincipalIdealRingstatement · cited by 131
- Valuedstatement and proof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- Valued.integer.isDiscreteValuationRing_of_compactSpaceproof · cited by 1