subobject_ofLE_as_imageToKernel — Mathlib

English

If w is a morphism equality f ≫ g = 0 and h is a relation showing a compatible subobject inclusion, then Subobject.ofLE(imageSubobject f, kernelSubobject g) h equals imageToKernel f g w.

Русский

Если есть равенство f ≫ g = 0 и отношение h, то Subobject.ofLE(imageSubobject f, kernelSubobject g) h равно imageToKernel f g w.

LaTeX

$$Subobject.ofLE (imageSubobject f) (kernelSubobject g) h = imageToKernel f g w$$

Lean4

/-- Prefer `imageToKernel`. -/
@[simp]
theorem subobject_ofLE_as_imageToKernel (w : f ≫ g = 0) (h) :
    Subobject.ofLE (imageSubobject f) (kernelSubobject g) h = imageToKernel f g w :=
  rfl

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