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theorem proved term proof

probability_sums_to_one

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formal statement (Lean)

 241theorem probability_sums_to_one (obs : Observer) :
 242    ∑ v : Fin obs.resolution, obs_probability obs v = 1 := by

proof body

Term-mode proof.

 243  simp only [obs_probability, Finset.sum_const, Finset.card_fin]
 244  rw [nsmul_eq_mul]
 245  have hN : (obs.resolution : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.pos_iff_ne_zero.mp obs.res_pos)
 246  field_simp [hN]
 247
 248/-- **Theorem (Probabilities are Non-negative)**:
 249    Each observation probability is non-negative. -/

depends on (10)

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