Theorems · Theorem · number theory
padicValNat_eq_emultiplicity
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {n : ℕ}, n ≠ 0 → ↑(padicValNat p n) = emultiplicity p nA simplification of padicValNat when one input is prime, by analogy with
padicValRat_def.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Fact.outproof · cited by 328
- emultiplicitystatement · cited by 156
- padicValNatstatement · cited by 106
- Nat.Prime.ne_oneproof · cited by 61
- padicValNat_eq_emultiplicity_of_ne_oneproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- padicValNat.pow_two_sub_powproof · cited by 1
- padicValNat_factorialproof · cited by 1
- one_le_padicValNat_of_dvdproof · cited by 1
- padicValNat.maxPowDiv_eq_emultiplicityproof · cited by 0
- padicValNat.pow_add_powproof · cited by 0
- padicValNat.pow_sub_powproof · cited by 0
- padicValNat_factorial_mulproof · cited by 0
- padicValNat_chooseproof · cited by 0
- padicValNat_choose'proof · cited by 0