equivInduced — Mathlib

English

An equivalence e between M and N induces a model-type equivalence between the corresponding induced structures.

Русский

Эквивалентность между M и N индуцирует эквивалентность моделей между индуцированными структурами.

LaTeX

$$$\text{equivInduced}(e) : M \to N \text{ is an equivalence of models under induced structure}$$$

Lean4

/-- Maps a bundled model along a bijection. -/
def equivInduced {M : ModelType.{u, v, w} T} {N : Type w'} (e : M ≃ N) : ModelType.{u, v, w'} T
    where
  Carrier := N
  struc := e.inducedStructure
  is_model := @StrongHomClass.theory_model L M N _ e.inducedStructure T _ _ _ e.inducedStructureEquiv _
  nonempty' := e.symm.nonempty

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