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formal statement (Lean)
111theorem fromSubsetSum_isSolution {n : ℕ} (weight : Fin n → ℤ) (target : ℤ)
112 (S : Finset (Fin n)) (h : (∑ i ∈ S, weight i) = target) :
113 isSolution (fromSubsetSum weight target) ⟨S⟩ := by
proof body
Term-mode proof.
114 constructor
115 · simpa [weightTarget, weightSum, fromSubsetSum] using h
116 constructor
117 · simp [residueNeutral, residueSum, fromSubsetSum]
118 · have hcost := fromSubsetSum_totalJCost_zero weight target S
119 change totalJCost (fromSubsetSum weight target) ⟨S⟩ ≤ 0
120 exact le_of_eq hcost
121
122end
123
124end BalancedJSubsetSum
125end Cryptography
126end IndisputableMonolith
depends on (13)
Lean names referenced from this declaration's body.
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weightSum
in IndisputableMonolith.Cost.Ndim.Calibration
decl_use
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fromSubsetSum
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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fromSubsetSum_totalJCost_zero
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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isSolution
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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residueNeutral
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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residueSum
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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totalJCost
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
-
weightSum
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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weightTarget
in IndisputableMonolith.Cryptography.BalancedJSubsetSum
decl_use
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isSolution
in IndisputableMonolith.Cryptography.ECDLPWatch
decl_use
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totalJCost
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
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totalJCost
in IndisputableMonolith.Information.ShannonEntropy
decl_use
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S
in IndisputableMonolith.Relativity.ILG.Action
decl_use