mk' — Mathlib

English

The same holds for mk' in the symmetrical formulation.

Русский

То же самое справедливо для mk' в симметричной формулировке.

LaTeX

$$theorem mk'_linear ...$$

Lean4

/-- Construct an affine map by verifying the relation between the map and its linear part at one
base point. Namely, this function takes a map `f : P₁ → P₂`, a linear map `f' : V₁ →ₗ[k] V₂`, and
a point `p` such that for any other point `p'` we have `f p' = f' (p' -ᵥ p) +ᵥ f p`. -/
def mk' (f : P1 → P2) (f' : V1 →ₗ[k] V2) (p : P1) (h : ∀ p' : P1, f p' = f' (p' -ᵥ p) +ᵥ f p) : P1 →ᵃ[k] P2
    where
  toFun := f
  linear := f'
  map_vadd' p' v := by rw [h, h p', vadd_vsub_assoc, f'.map_add, vadd_vadd]

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