sub_comp — Mathlib

English

For a fixed c and natural n, smulRight 1 c raised to n equals smulRight 1 (c^n).

Русский

При фиксированном c и натуральном n справедливо (smulRight 1 c)^n = smulRight 1 (c^n).

LaTeX

$$smulRight 1 c ^ n = smulRight 1 (c ^ n)$$

Lean4

@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [IsTopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
    (f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f :=
  by
  ext
  simp

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