Theorems · Theorem · logic and foundations
FirstOrder.Language.Equiv.apply_symm_apply
∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N] (f : L.Equiv M N)
(a : N), f (f.symm a) = a- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Equiv.apply_symm_applyproof · cited by 346
- FirstOrder.Language.Equivstatement and proof · cited by 83
- FirstOrder.Language.Equiv.symmstatement · cited by 32
- FirstOrder.Language.Equiv.toEquivproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.PartialEquiv.cod_le_codproof · cited by 6
- FirstOrder.Language.Equiv.self_comp_symmproof · cited by 3
- FirstOrder.Language.IsUltrahomogeneous.extend_embeddingproof · cited by 2
- FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion_applyproof · cited by 1
- FirstOrder.Language.PartialEquiv.symm_le_symmproof · cited by 1
- FirstOrder.Language.Equiv.toHom_rangeproof · cited by 0