Theorems · Definition · logic and foundations
FirstOrder.Language.Formula.exClosure
{L : FirstOrder.Language} → {α : Type u'} → [DecidableEq α] → L.Formula α → L.SentenceexClosure φ is the sentence asserting that there exist values for all free variables of φ
such that φ holds.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.Formulastatement and proof · cited by 93
- FirstOrder.Language.BoundedFormula.freeVarFinsetproof · cited by 9
- FirstOrder.Language.Formula.iExsproof · cited by 8
- FirstOrder.Language.BoundedFormula.restrictFreeVarproof · cited by 7
- FirstOrder.Language.Formula.relabelproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Formula.realize_exClosurestatement · cited by 2
- FirstOrder.Language.Formula.realize_exClosure_of_realize_equivSentencestatement · cited by 0
- FirstOrder.Language.Formula.exClosure.congr_simpstatement and proof · cited by 0
- FirstOrder.Language.Formula.exists_realize_equivSentence_iff_realize_exClosurestatement and proof · cited by 0