ofIsLimitKernelFork_f' — Mathlib

English

Given hf : S.f = 0, and a kernel fork (c hc) that is an isLimit, the constructed f' component vanishes: (ofIsLimitKernelFork S hf c hc).f' = 0.

Русский

При hf: S.f = 0 и ядро-ответвление (c hc) как IsLimit, компонент f' равен нулю: (ofIsLimitKernelFork S hf c hc).f' = 0.

LaTeX

$$$ (ofIsLimitKernelFork S hf c hc).f' = 0 $$$

Lean4

@[simp]
theorem ofIsLimitKernelFork_f' (hf : S.f = 0) (c : KernelFork S.g) (hc : IsLimit c) :
    (ofIsLimitKernelFork S hf c hc).f' = 0 := by
  rw [← cancel_mono (ofIsLimitKernelFork S hf c hc).i, f'_i, hf, zero_comp]

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