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Theorems · Definition · number theory

padicValRat

ℕ → ℚ → ℤ

padicValRat defines the valuation of a rational q to be the valuation of q.num minus the valuation of q.den. If q = 0 or p = 1, then padicValRat p q defaults to 0.

Defined in
Mathlib.NumberTheory.Padics.PadicVal.Basic
Cited by
49 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

padicNorm · cited by 83padicNormRat.padicValuation · cited by 18Rat.padicValuationpadicNorm.zero · cited by 11padicNorm.zeropadicValRat.of_nat · cited by 9padicValRat.of_natpadicNorm.eq_zpow_of_nonzero · cited by 7padicNorm.eq_zpow_of_nonz…padicValRat.of_int · cited by 7padicValRat.of_intpadicValNat.mul · cited by 6padicValNat.mulPadic.norm_p · cited by 5Padic.norm_ppadicNorm.nonarchimedean · cited by 5padicNorm.nonarchimedeanpadicValRat.inv · cited by 5padicValRat.invpadicValRat.mul · cited by 5padicValRat.mulpadicValRat.one · cited by 5padicValRat.onepadicValRat.zero · cited by 5padicValRat.zeropadicValRat.pow · cited by 4padicValRat.powpadicNorm.int_eq_one_iff · cited by 3padicNorm.int_eq_one_iffpadicValNat · cited by 106padicValNatpadicValInt · cited by 22padicValIntpadicValRatCITED BYCITES

Cites2

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Cited by52

Results whose statement or proof uses this declaration.