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Theorems · Theorem · number theory

PadicInt.valuation_mul

∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {x y : ℤ_[p]}, x ≠ 0 → y ≠ 0 → (x * y).valuation = x.valuation + y.valuation
Defined in
Mathlib.NumberTheory.Padics.PadicIntegers
Cited by
1 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Fact
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PadicInt.valuation_p_pow_mul · cited by 2PadicInt.valuation_p_pow_…Fact · cited by 2726FactNat.Prime · cited by 2059Nat.PrimeNat.cast_add · cited by 586Nat.cast_addPadicInt · cited by 179PadicIntPadic.valuation · cited by 28Padic.valuationPadicInt.valuation · cited by 19PadicInt.valuationPadicInt.coe_ne_zero · cited by 4PadicInt.coe_ne_zeroPadic.valuation_mul · cited by 2Padic.valuation_mulPadicInt.valuation_mulCITED BYCITES

Cites8

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Cited by1

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