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theorem proved term proof

quark_preds_pos

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formal statement (Lean)

 365theorem quark_preds_pos :
 366    0 < up_quark_pred ∧ 0 < charm_quark_pred ∧ 0 < top_quark_pred := by

proof body

Term-mode proof.

 367  unfold up_quark_pred charm_quark_pred top_quark_pred
 368  refine ⟨div_pos (pow_pos Constants.phi_pos _) (by norm_num),
 369          div_pos (pow_pos Constants.phi_pos _) (by norm_num),
 370          div_pos (pow_pos Constants.phi_pos _) (by norm_num)⟩
 371
 372/-- The charm/up ratio equals φ^11 exactly (11-rung generation gap). -/

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