Theorems · Theorem · number theory

NumberField.Units.dirichletUnitTheorem.seq_next

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (w₁ : NumberField.InfinitePlace K) {B : ℕ},
  NumberField.mixedEmbedding.minkowskiBound K 1 < ↑(NumberField.mixedEmbedding.convexBodyLTFactor K) * ↑B →
    ∀ {x : NumberField.RingOfIntegers K},
      x ≠ 0 → ∃ y, y ≠ 0 ∧ (∀ (w : NumberField.InfinitePlace K), w ≠ w₁ → w ↑y < w ↑x) ∧ |(Algebra.norm ℚ) ↑y| ≤ ↑B

This result shows that there always exists a next term in the sequence.

Defined in: Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by: 3 results in Mathlib
Foundations: Depth 313 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cited by3

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NumberField.Units.dirichletUnitTheorem.seq_norm_leproof · cited by 1
NumberField.Units.dirichletUnitTheorem.seq_decreasingproof · cited by 1
NumberField.Units.dirichletUnitTheorem.seq.eq_defproof · cited by 0