apply_apply' — Mathlib

English

If f is a continuous map X → E →SL[σ₁₂] F and g is a continuous map F →SL[σ₂₃] G, then x ↦ g ∘ (f x) is continuous.

Русский

Если f: X → E →SL[σ₁₂] F и g: F →SL[σ₂₃] G непрерывны, то x ↦ g ∘ f x непрерывно.

LaTeX

$$$ \\text{Continuous } f \\Rightarrow \\text{Continuous } (x \\mapsto g \\circ (f x)) $$$

Lean4

@[simp]
theorem apply_apply' (v : E) (f : E →SL[σ₁₂] F) : apply' F σ₁₂ v f = f v :=
  rfl

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