Theorems · Theorem · number theory
padicValRat.le_padicValRat_add_of_le
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {q r : ℚ},
q + r ≠ 0 → padicValRat p q ≤ padicValRat p r → padicValRat p q ≤ padicValRat p (q + r)Sufficient conditions to show that the p-adic valuation of q is less than or equal to the
p-adic valuation of q + r.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Factstatement and proof · cited by 2,726
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
- add_commproof · cited by 1,535
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- add_mulproof · cited by 363
Cited by1
Results whose statement or proof uses this declaration.
- padicValRat.min_le_padicValRat_addproof · cited by 3