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theorem proved term proof

spatialRadius_pos_of_ne_zero

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formal statement (Lean)

 162theorem spatialRadius_pos_of_ne_zero (x : Fin 4 → ℝ) (hx : spatialRadius x ≠ 0) :
 163    0 < spatialRadius x := by

proof body

Term-mode proof.

 164  have h_ne : spatialNormSq x ≠ 0 := (spatialRadius_ne_zero_iff x).mp hx
 165  exact (spatialRadius_pos_iff x).2 (lt_of_le_of_ne (spatialNormSq_nonneg x) h_ne.symm)
 166
 167/-- Temporal coordinate ray doesn't change spatial components. -/

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