Theorems · Theorem · logic and foundations
FirstOrder.Language.Equiv.fg_iff
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : Type u_2} [inst_1 : L.Structure N]
(f : L.Equiv M N), FirstOrder.Language.Structure.FG L M ↔ FirstOrder.Language.Structure.FG L N- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.symmproof · cited by 3,681
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Equiv.surjectiveproof · cited by 198
- FirstOrder.Language.Equivstatement and proof · cited by 83
- FirstOrder.Language.Equiv.symmproof · cited by 32
- FirstOrder.Language.Structure.FGstatement and proof · cited by 27
- FirstOrder.Language.Equiv.toEquivproof · cited by 12
- FirstOrder.Language.Equiv.toHomproof · cited by 11
- FirstOrder.Language.Structure.FG.map_of_surjectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.FG.mem_age_of_equivproof · cited by 1
- FirstOrder.Language.age.is_equiv_invariantproof · cited by 1
- FirstOrder.Language.PartialEquiv.dom_fg_iff_cod_fgproof · cited by 0