cast — Mathlib

English

The composition map that sends t to the evaluation of (F.trans G) at t is continuous.

Русский

Композиция, отправляющая t в значение (F.trans G) на t, непрерывна.

LaTeX

$$$t \\mapsto (F.trans G)(t, x)$ is continuous for each x.$$

Lean4

/-- Casting a `HomotopyWith f₀ f₁ P` to a `HomotopyWith g₀ g₁ P` where `f₀ = g₀` and `f₁ = g₁`.
-/
@[simps!]
def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (h₀ : f₀ = g₀) (h₁ : f₁ = g₁) : HomotopyWith g₀ g₁ P
    where
  toHomotopy := F.toHomotopy.cast h₀ h₁
  prop' := F.prop

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