Theorems · Theorem · commutative algebra
Valuation.one_apply_le_one
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] [inst_2 : Nontrivial R]
[inst_3 : NoZeroDivisors R] [inst_4 : DecidablePred fun x => x = 0] (x : R), 1 x ≤ 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- Valuationstatement · cited by 823
- NoZeroDivisorsstatement and proof · cited by 545
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.one_apply_defproof · cited by 2
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