Theorems · Theorem · logic and foundations
FirstOrder.Language.Equiv.symm_apply_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 : M), f.symm (f a) = a- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 3 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.symm_apply_applyproof · cited by 320
- FirstOrder.Language.Equivstatement and proof · cited by 83
- FirstOrder.Language.Equiv.symmstatement · cited by 32
- FirstOrder.Language.Equiv.toEquivproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Equiv.symm_comp_selfproof · cited by 2
- FirstOrder.Language.IsUltrahomogeneous.amalgamation_ageproof · cited by 1
- FirstOrder.Language.PartialEquiv.symm_le_symmproof · cited by 1