theorem
proved
term proof
spatialRadius_pos_of_ne_zero
show as:
view Lean formalization →
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. -/
used by (10)
-
laplacian_radialInv_n -
laplacian_radialInv_zero_no_const -
partialDeriv_v2_radialInv -
secondDeriv_radialInv -
spatialRadius_coordRay_ne_zero -
laplacian_radialInv_n_proved -
laplacian_radialInv_zero_no_const_proved -
partialDeriv_v2_radialInv_proved -
secondDeriv_radialInv_proved -
spatialRadius_coordRay_ne_zero_proved