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formal statement (Lean)
158@[simp] theorem involutionOp_single (v : MultIndex) (c : ℝ) :
159 involutionOp (Finsupp.single v c) = Finsupp.single (-v) c := by
proof body
Term-mode proof.
160 simp [involutionOp, Finsupp.lmapDomain_apply, Finsupp.mapDomain_single]
161
162/-! ## Structural theorems -/
163
164/-- The reciprocal involution is involutive: `U ∘ U = id`. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (13)
Lean names referenced from this declaration's body.
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id
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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reciprocal
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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U
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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id
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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reciprocal
in IndisputableMonolith.Foundation.LedgerForcing
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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involutionOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
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MultIndex
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
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U
in IndisputableMonolith.Recognition
decl_use
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id
in IndisputableMonolith.RRF.Core.Octave
decl_use