Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Field.FieldAxiom.toSentence

FirstOrder.Field.FieldAxiom → FirstOrder.Language.ring.Sentence

The first-order sentence corresponding to each field axiom

Defined in
Mathlib.ModelTheory.Algebra.Field.Basic
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Quot.sound
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Around this declaration

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

FirstOrder.Language.Theory.field · cited by 6Theory.fieldFirstOrder.Field.FieldAxiom.realize_toSentence_iff_toProp · cited by 1FieldAxiom.realize_toSent…FirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.ring · cited by 36Language.ringFirstOrder.Language.BoundedFormula.not · cited by 27BoundedFormula.notFirstOrder.Language.BoundedFormula.ex · cited by 14BoundedFormula.exFirstOrder.Field.FieldAxiom · cited by 11Field.FieldAxiomFirstOrder.Language.Term.bdEqual · cited by 10Term.bdEqualFieldAxiom.toSentenceCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.