def definition def or abbrev

`isBalanced`

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

formal statement (Lean)

  41def isBalanced (S : StrainFunctional State) (x : State) : Prop :=

proof body

Definition body.

  42  S.J x = 0
  43
  44/-- The set of equilibrium states. -/

used by (23)

From the project-wide theorem graph. These declarations reference this one in their body.

isBalanced in IndisputableMonolith.Cosmology.DarkEnergy decl_use
isBalanced in IndisputableMonolith.RRF.Core.Glossary decl_use
isConsistent in IndisputableMonolith.RRF.Core.Glossary decl_use
JMinimizationLaw in IndisputableMonolith.RRF.Core.Glossary decl_use
V in IndisputableMonolith.RRF.Core.Glossary decl_use
preserves_equilibria in IndisputableMonolith.RRF.Core.Octave decl_use
wellPosed in IndisputableMonolith.RRF.Core.Octave decl_use
equilibria in IndisputableMonolith.RRF.Core.Strain decl_use
equilibria_are_minimizers in IndisputableMonolith.RRF.Core.Strain decl_use
hasUniqueMin in IndisputableMonolith.RRF.Core.Strain decl_use
isValid in IndisputableMonolith.RRF.Core.Strain decl_use
equilibria in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use
equilibria_iso in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use
hasEquilibrium in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use
isBalanced in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use
preserves_balanced in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use
quadratic1D_equilibrium in IndisputableMonolith.RRF.Models.Quadratic decl_use
quadratic1D_unique_equilibrium in IndisputableMonolith.RRF.Models.Quadratic decl_use
shifted_equilibrium in IndisputableMonolith.RRF.Models.Quadratic decl_use
trivial_balanced in IndisputableMonolith.RRF.Models.Trivial decl_use
equiv_equilibria_iff in IndisputableMonolith.RRF.Theorems.OctaveTransfer decl_use
equiv_wellPosed in IndisputableMonolith.RRF.Theorems.OctaveTransfer decl_use
equilibria_minimal in IndisputableMonolith.RRF.Theorems.OrderPreservation decl_use

depends on (13)

Lean names referenced from this declaration's body.

of in IndisputableMonolith.Astrophysics.NucleosynthesisTiers decl_use
State in IndisputableMonolith.ClassicalBridge.Fluids.CPM2D decl_use
isBalanced in IndisputableMonolith.Cosmology.DarkEnergy decl_use
of in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization decl_use
of in IndisputableMonolith.Foundation.PhiForcingDerived decl_use
of in IndisputableMonolith.Foundation.SpectralEmergence decl_use
of in IndisputableMonolith.Information.PhysicsComplexityStructure decl_use
State in IndisputableMonolith.NavierStokes.DiscreteVorticity decl_use
equilibrium in IndisputableMonolith.Physics.NonlinearDynamicsFromRS decl_use
S in IndisputableMonolith.Relativity.ILG.Action decl_use
isBalanced in IndisputableMonolith.RRF.Core.Glossary decl_use
StrainFunctional in IndisputableMonolith.RRF.Core.Strain decl_use
isBalanced in IndisputableMonolith.RRF.Foundation.VantageCategory decl_use