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lemma proved term proof

spatialNormSq_coordRay_spatial_2

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formal statement (Lean)

 210private lemma spatialNormSq_coordRay_spatial_2 (x : Fin 4 → ℝ) (s : ℝ) :
 211    spatialNormSq (coordRay x 2 s) = x 1 ^ 2 + (x 2 + s) ^ 2 + x 3 ^ 2 := by

proof body

Term-mode proof.

 212  unfold spatialNormSq coordRay basisVec
 213  rw [if_neg (by decide : (1 : Fin 4) ≠ 2),
 214      if_pos (rfl : (2 : Fin 4) = 2),
 215      if_neg (by decide : (3 : Fin 4) ≠ 2)]
 216  ring
 217

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