Theorems · Definition · logic and foundations
FirstOrder.Language.LEquiv.trans
{L : FirstOrder.Language} →
{L' : FirstOrder.Language} → {L'' : FirstOrder.Language} → (L ≃ᴸ L') → (L' ≃ᴸ L'') → (L ≃ᴸ L'')The composition of equivalences of first-order languages.
- Defined in
- Mathlib.ModelTheory.LanguageMap
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.LHom.compproof · cited by 20
- FirstOrder.Language.LEquivstatement and proof · cited by 19
- FirstOrder.Language.LEquiv.toLHomproof · cited by 11
- FirstOrder.Language.LEquiv.invLHomproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.LEquiv.trans_invLHomstatement and proof · cited by 0
- FirstOrder.Language.LEquiv.trans_toLHomstatement and proof · cited by 0