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theorem proved term proof

middle_pair_sum_forced

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formal statement (Lean)

  63theorem middle_pair_sum_forced (a b c d : ℕ)
  64    (hsum : a + b + c + d = 38)
  65    (hpart : partition_sum a b c d = 55) :
  66    b + c = 17 := by

proof body

Term-mode proof.

  67  have := partition_sum_decomp a b c d
  68  omega
  69
  70/-! ## Step 2: Uniqueness — Only {11, 6} sums to 17
  71
  72Among the four values {13, 11, 6, 8}, the only pair summing to 17
  73is {11, 6} = {E_pass, F}. -/
  74
  75/-- Exhaustive check: no other pair from {13, 11, 6, 8} sums to 17. -/

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