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lemma proved term proof

spatialNormSq_coordRay_spatial_1

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formal statement (Lean)

 202private lemma spatialNormSq_coordRay_spatial_1 (x : Fin 4 → ℝ) (s : ℝ) :
 203    spatialNormSq (coordRay x 1 s) = (x 1 + s) ^ 2 + x 2 ^ 2 + x 3 ^ 2 := by

proof body

Term-mode proof.

 204  unfold spatialNormSq coordRay basisVec
 205  rw [if_pos (rfl : (1 : Fin 4) = 1),
 206      if_neg (by decide : (2 : Fin 4) ≠ 1),
 207      if_neg (by decide : (3 : Fin 4) ≠ 1)]
 208  ring
 209

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