Theorems · Theorem · logic and foundations
FirstOrder.Language.Equiv.comp_apply
∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N] {P : Type u_1}
[inst_2 : L.Structure P] (g : L.Equiv N P) (f : L.Equiv M N) (x : M), (g.comp f) x = g (f x)- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Equivstatement and proof · cited by 83
- FirstOrder.Language.Equiv.compstatement · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Equiv.self_comp_symmproof · cited by 3
- FirstOrder.Language.Equiv.symm_comp_selfproof · cited by 2