Mathlib Map

Theorems · Inductive type · logic and foundations

FirstOrder.Field.FieldAxiom

Type

An indexing type to name each of the field axioms. The theory of fields is defined as the range of a function FieldAxiom -> Language.ring.Sentence

Defined in
Mathlib.ModelTheory.Algebra.Field.Basic
Cited by
11 results in Mathlib
Foundations
Depth 0 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Field.FieldAxiom.toProp · cited by 2FieldAxiom.toPropFirstOrder.Field.FieldAxiom.realize_toSentence_iff_toProp · cited by 1FieldAxiom.realize_toSent…FirstOrder.Field.FieldAxiom.toSentence · cited by 1FieldAxiom.toSentenceFirstOrder.Field.FieldAxiom.casesOn · cited by 1FieldAxiom.casesOnFirstOrder.Field.FieldAxiom.ctorIdx · cited by 0FieldAxiom.ctorIdxFirstOrder.Field.FieldAxiom.noConfusion · cited by 0FieldAxiom.noConfusionFirstOrder.Field.FieldAxiom.noConfusionType · cited by 0FieldAxiom.noConfusionTypeFirstOrder.Field.FieldAxiom.recOn · cited by 0FieldAxiom.recOnFirstOrder.Field.FieldAxiom.toCtorIdx · cited by 0FieldAxiom.toCtorIdxFirstOrder.Field.FieldAxiom.toProp_of_model · cited by 0FieldAxiom.toProp_of_modelFirstOrder.Field.FieldAxiom.addAssoc.elim · cited by 0addAssoc.elimFirstOrder.Field.FieldAxiom.addAssoc.sizeOf_spec · cited by 0addAssoc.sizeOf_specFirstOrder.Field.FieldAxiom.existsInv.elim · cited by 0existsInv.elimFirstOrder.Field.FieldAxiom.existsInv.sizeOf_spec · cited by 0existsInv.sizeOf_specFirstOrder.Field.FieldAxiom.existsPairNE.elim · cited by 0existsPairNE.elimField.FieldAxiomCITED BYCITES

Cites0

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Nothing in Mathlib beyond the foundations.

Cited by30

Results whose statement or proof uses this declaration.