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theorem proved term proof

affineShift_mem_LevelSet

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formal statement (Lean)

 103theorem affineShift_mem_LevelSet {n : ℕ} (α : Vec n) {c s : ℝ} {t v : Vec n}
 104    (ht : t ∈ LevelSet α c) (hv : v ∈ Radical α) :
 105    affineShift t v s ∈ LevelSet α c := by

proof body

Term-mode proof.

 106  rw [mem_LevelSet_iff] at ht ⊢
 107  have hv' : dot α v = 0 := hv
 108  rw [dot_affineShift, ht, hv']
 109  ring
 110
 111/-- The radical distribution is integrable: its integral leaves are the affine
 112hyperplanes `dot α = c`. -/

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