symm_apply — Mathlib

English

If X ≃ₕ Y and Y ≃ₕ Z, then (X ≃ₕ Y) trans (Y ≃ₕ Z) inverse equals the inverse of the composed.

Русский

Если X ≃ₕ Y и Y ≃ₕ Z, то (X ≃ₕ Y) trans (Y ≃ₕ Z).symm = Z ≃ₕ Y trans X ≃ₕ Y.

LaTeX

$$$(h_1: X\simeq_h Y) (h_2: Y\simeq_h Z) \Rightarrow (h_1.trans h_2).symm = h_2.symm.trans h_1.symm$$

Lean4

/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
because it is a composition of multiple projections. -/
def symm_apply (h : X ≃ₕ Y) : Y → X :=
  h.symm

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