Theorems · Theorem · number theory
Padic.le_valuation_add
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {x y : ℚ_[p]}, x + y ≠ 0 → min x.valuation y.valuation ≤ (x + y).valuation- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Norm.normproof · cited by 5,413
- Factstatement and proof · cited by 2,726
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.Primestatement and proof · cited by 2,059
- Fact.outproof · cited by 328
- Padicstatement and proof · cited by 151
- Nat.Prime.one_ltproof · cited by 118
- min_le_leftproof · cited by 105
- min_le_rightproof · cited by 88
- Padic.valuationstatement and proof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.le_valuation_addproof · cited by 0
- Padic.AddValuation.map_addproof · cited by 0