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formal statement (Lean)
229theorem pc_implies_peeling {n}
230 (inputs : InputSet n) (aRef : Assignment n) (φ : CNF n) (H : XORSystem n) :
231 PC inputs aRef φ H → PeelingWitness inputs aRef φ H := by
proof body
Term-mode proof.
232 intro hPC
233 let result := buildPeelingResult inputs aRef φ H hPC inputs (fun _ h => h)
234 exact ⟨{
235 vars := result.vars
236 constrs := result.constrs
237 nodup := result.nodup
238 len_eq := result.len_eq
239 cover := fun v => (result.cover v).symm
240 step := result.step
241 }⟩
242
243/-- Peeling ⇒ forced arborescence (Prop-level).
244 Trivial since ForcedArborescence is defined as PeelingWitness. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
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H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
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Assignment
in IndisputableMonolith.Complexity.RSatEncoding
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Assignment
in IndisputableMonolith.Complexity.SAT.CNF
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CNF
in IndisputableMonolith.Complexity.SAT.CNF
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buildPeelingResult
in IndisputableMonolith.Complexity.SAT.PC
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ForcedArborescence
in IndisputableMonolith.Complexity.SAT.PC
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InputSet
in IndisputableMonolith.Complexity.SAT.PC
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PC
in IndisputableMonolith.Complexity.SAT.PC
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PeelingWitness
in IndisputableMonolith.Complexity.SAT.PC
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XORSystem
in IndisputableMonolith.Complexity.SAT.XOR
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H
in IndisputableMonolith.Cost.FunctionalEquation
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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as
in IndisputableMonolith.Foundation.SimplicialLedger.ContinuumBridge
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use