Theorems · Definition · number theory
NumberField.RingOfIntegers.val
{K : Type u_1} → [inst : Field K] → NumberField.RingOfIntegers K → KThe canonical coercion from 𝓞 K to K.
- Defined in
- Mathlib.NumberTheory.NumberField.Basic
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- NumberField.RingOfIntegersstatement and proof · cited by 413
Cited by75
Results whose statement or proof uses this declaration.
- NumberField.RingOfIntegers.extstatement and proof · cited by 10
- NumberField.RingOfIntegers.ext_iffstatement and proof · cited by 8
- Algebra.coe_norm_intstatement · cited by 5
- NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSetstatement and proof · cited by 5
- NumberField.RingOfIntegers.coe_eq_algebraMapstatement · cited by 4
- NumberField.mixedEmbedding.fundamentalCone.mem_integerSetstatement and proof · cited by 4
- NumberField.is_primitive_element_of_infinitePlace_ltstatement and proof · cited by 3
- NumberField.FinitePlace.hasFiniteMulSupport_intstatement and proof · cited by 3
- NumberField.Units.dirichletUnitTheorem.seq_nextstatement and proof · cited by 3
- NumberField.abs_discr_ge'proof · cited by 2
- NumberField.finite_setOfPred_prod_infinitePlace_iSup_lestatement and proof · cited by 2
- NumberField.Units.mem_torsionproof · cited by 2