Theorems · Theorem · number theory

NumberField.mem_span_basisOfFractionalIdeal

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  {I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ} {x : K},
  x ∈ Submodule.span ℤ (Set.range ⇑(NumberField.basisOfFractionalIdeal K I)) ↔ x ∈ ↑↑I

Defined in: Mathlib.NumberTheory.NumberField.FractionalIdeal
Cited by: 0 results in Mathlib
Foundations: Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
SetLike.coestatement and proof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Unitsstatement and proof · cited by 2,804
Units.valstatement and proof · cited by 1,966
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement and proof · cited by 1,477
nonZeroDivisorsstatement and proof · cited by 895
NumberFieldstatement and proof · cited by 653

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