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theorem proved tactic proof

proper_time_from_velocity

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formal statement (Lean)

 268theorem proper_time_from_velocity (v : Displacement)
 269    (ht : v ⟨0, by omega⟩ ≠ 0) :
 270    proper_time_sq v = temporal_sq v * (1 - velocity_sq v ht) := by

proof body

Tactic-mode proof.

 271  have h_ne : temporal_sq v ≠ 0 := by unfold temporal_sq; exact pow_ne_zero 2 ht
 272  suffices temporal_sq v * (1 - spatial_norm_sq v / temporal_sq v) =
 273      temporal_sq v - spatial_norm_sq v by
 274    simp only [proper_time_sq, velocity_sq]; linarith
 275  field_simp [h_ne]
 276
 277/-- **Subluminal velocity for timelike**: τ² > 0 iff v² < 1. -/

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