setCongr — Mathlib

English

If s = t, then the identity homeomorphism between s and t is continuous.

Русский

Если s = t, то тождественное гомеоморфизм между s и t непрерывен.

LaTeX

$$$Set.inclusion \\circ id = id \\circ Set.inclusion$$$

Lean4

/-- If two sets are equal, then they are homeomorphic. -/
def setCongr {s t : Set X} (h : s = t) : s ≃ₜ t
    where
  continuous_toFun := continuous_inclusion h.subset
  continuous_invFun := continuous_inclusion h.symm.subset
  toEquiv := Equiv.setCongr h

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