No prose has been written for this declaration yet. The Lean source and graph data below render
without it.
generate prose now
formal statement (Lean)
517theorem equilibrium_iff_minimizer {N : ℕ}
518 (c : Configuration N) :
519 IsEquilibrium c ↔ ∀ c' ∈ Feasible c, total_defect c ≤ total_defect c' := by
proof body
Term-mode proof.
520 constructor
521 · intro ⟨_, hmin⟩
522 exact hmin
523 · intro hmin
524 exact ⟨self_feasible c, hmin⟩
525
526/-- **Theorem**: The unity configuration is an equilibrium when log-charge = 0. -/
depends on (11)
Lean names referenced from this declaration's body.
-
Configuration
in IndisputableMonolith.Foundation.InitialCondition
decl_use
-
total_defect
in IndisputableMonolith.Foundation.InitialCondition
decl_use
-
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
-
Configuration
in IndisputableMonolith.Foundation.RecognitionForcing
decl_use
-
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
-
Feasible
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
IsEquilibrium
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
self_feasible
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
-
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
-
equilibrium
in IndisputableMonolith.Physics.NonlinearDynamicsFromRS
decl_use