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theorem proved term proof

unsat_positive_jcost

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formal statement (Lean)

 139theorem unsat_positive_jcost {n : ℕ} (f : CNFFormula n) (h : f.isUNSAT) :
 140    ∀ a : Assignment n, satJCost f a > 0 := by

proof body

Term-mode proof.

 141  intro a
 142  have := h a
 143  by_contra hle
 144  push_neg at hle
 145  have heq : satJCost f a = 0 := le_antisymm hle (satJCost_nonneg f a)
 146  rw [satJCost_zero_iff] at heq
 147  exact absurd heq (by simp [this])
 148
 149/-- The topological obstruction: for UNSAT formulas, the minimum J-cost over
 150    all assignments is positive (bounded away from zero). -/

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