ker_inr — Mathlib

English

Let f: M → M₃ and g: M₂ → M₃. Then ker(f.coprod g) equals (ker f) × (ker g) when ranges are disjoint.

Русский

Пусть f: M → M₃ и g: M₂ → M₃. Тогда ker(f.coprod g) = (ker f) × (ker g) при независимости образов.

LaTeX

$$$\\ker(f \\ coprod\\ g) = (\\ker f) \\ times (\\ker g)\\quad\\text{if }\\mathrm{range}(f) \\cap \\mathrm{range}(g) = \\{0\\}$$$

Lean4

@[simp]
theorem ker_inr : ker (inr R M M₂) = ⊥ := by rw [ker, ← prod_bot, prod_comap_inr]

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