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formal statement (Lean)
183theorem quarticRemainder_nonneg {n : ℕ} (G : WeightedLedgerGraph n)
184 (ε : LogPotential n) : 0 ≤ quarticRemainder G ε := by
proof body
Term-mode proof.
185 unfold quarticRemainder
186 apply Finset.sum_nonneg
187 intro i _
188 apply Finset.sum_nonneg
189 intro j _
190 exact mul_nonneg (G.weight_nonneg i j) (coshRemainder_nonneg _)
191
192/-- Helper: the laplacian action as the product-sum of quadratic terms. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (15)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
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G
in IndisputableMonolith.Constants
decl_use
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G
in IndisputableMonolith.Constants.Codata
decl_use
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G
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
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as
in IndisputableMonolith.Foundation.SimplicialLedger.ContinuumBridge
decl_use
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WeightedLedgerGraph
in IndisputableMonolith.Foundation.SimplicialLedger.ContinuumBridge
decl_use
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LogPotential
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
-
coshRemainder_nonneg
in IndisputableMonolith.Foundation.SimplicialLedger.NonlinearBridge
decl_use
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quarticRemainder
in IndisputableMonolith.Foundation.SimplicialLedger.NonlinearBridge
decl_use
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of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
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G
in IndisputableMonolith.Gravity.JCostInflaton
decl_use
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
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laplacian
in IndisputableMonolith.Relativity.Calculus.Derivatives
decl_use