Theorems · Theorem · field theory
Field.toIsField
∀ (R : Type u) [inst : Field R], IsField R
Transferring from Field to IsField.
- Defined in
- Mathlib.Algebra.Field.IsField
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- IsFieldstatement · cited by 103
- Semifield.toIsFieldproof · cited by 1
Cited by18
Results whose statement or proof uses this declaration.
- Ideal.Quotient.maximal_ideal_iff_isField_quotientproof · cited by 7
- Polynomial.induction_of_Splits_of_injective_of_surjectiveproof · cited by 4
- IsLocalRing.maximalIdeal_eq_botproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- IsBaseChange.lift_rank_eqproof · cited by 3
- Finite.isField_of_domainproof · cited by 3
- IsFractionRing.surjective_iff_isFieldproof · cited by 2
- Algebra.TensorProduct.isField_of_isAlgebraicproof · cited by 2
- Polynomial.not_weaklyQuasiFiniteAtproof · cited by 2
- IsLocalRing.finrank_cotangentSpace_eq_zeroproof · cited by 1
- AlgebraicGeometry.isField_of_universallyClosedproof · cited by 1
- IsArtinianRing.isField_of_isReduced_of_isLocalRingproof · cited by 1