Theorems · Theorem · number theory
Rat.AbsoluteValue.not_real_isEquiv_padic
∀ (p : ℕ) [inst : Fact (Nat.Prime p)], ¬Rat.AbsoluteValue.real.IsEquiv (Rat.AbsoluteValue.padic p)
The standard absolute value on ℚ is not equivalent to any p-adic absolute value.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- LE.le.trans_ltproof · cited by 795
- one_lt_twoproof · cited by 67
- AbsoluteValue.IsEquivstatement · cited by 32
- Rat.cast_ofNatproof · cited by 19
- Nat.abs_ofNatproof · cited by 12
- Rat.AbsoluteValue.padicstatement and proof · cited by 6
- Rat.AbsoluteValue.realstatement and proof · cited by 4
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