Theorems · Theorem · number theory
padicValRat.defn
∀ (p : ℕ) [hp : Fact (Nat.Prime p)] {q : ℚ} {n d : ℤ},
q ≠ 0 → q = Rat.divInt n d → padicValRat p q = ↑(multiplicity (↑p) n) - ↑(multiplicity (↑p) d)A rewrite lemma for padicValRat p q when q is expressed in terms of Rat.mk.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_addproof · cited by 586
- Fact.outproof · cited by 328
- multiplicitystatement and proof · cited by 117
- Nat.Prime.ne_oneproof · cited by 61
- padicValRatstatement and proof · cited by 49
- Nat.prime_iff_prime_intproof · cited by 27
- multiplicity_mulproof · cited by 5
- Rat.num_den_mkproof · cited by 2
- Int.natCast_multiplicityproof · cited by 1
- padicValRat.multiplicity_sub_multiplicityproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- padicValRat.mulproof · cited by 5
- padicValRat.padicValRat_le_padicValRat_iffproof · cited by 1