English
Reparametrizing the constant path (refl x) by any f with f(0)=0 and f(1)=1 yields the same constant path; i.e., (refl x).reparam f hfcont hf0 hf1 = refl x.
Русский
Переparametrизация константного пути (refl x) любой f с f(0)=0 и f(1)=1 даёт тот же константный путь; то есть (refl x).reparam f = refl x.
LaTeX
$$$ (\mathrm{refl}\ x).reparam(f) = \mathrm{refl}\ x $$$
Lean4
theorem refl_reparam {f : I → I} (hfcont : Continuous f) (hf₀ : f 0 = 0) (hf₁ : f 1 = 1) :
(refl x).reparam f hfcont hf₀ hf₁ = refl x := by
ext
simp