def definition def or abbrev

`GateFails`

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

formal statement (Lean)

  19def GateFails (n c : ℕ) : Prop :=

proof body

Definition body.

  20  ¬ HitsBalancedPhase n c
  21
  22/-- An abstract cost assignment for a failed gate.  The positivity field is
  23the only property needed for the finite accumulation theorems. -/

used by (8)

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

failed_gate_count_bounded_at_KTheta in IndisputableMonolith.NumberTheory.BoundedPhaseVisibility decl_use
KThetaFailureFloorHypothesis in IndisputableMonolith.NumberTheory.BoundedPhaseVisibility decl_use
GateFailureCost in IndisputableMonolith.NumberTheory.PhaseFailureCost decl_use
phase_failure_accumulates in IndisputableMonolith.NumberTheory.PhaseFailureCost decl_use
phase_failure_accumulates_packaged in IndisputableMonolith.NumberTheory.PhaseFailureCost decl_use
phase_failure_cost_lower_bound in IndisputableMonolith.NumberTheory.PhaseFailureCost decl_use
UniformFailureFloor in IndisputableMonolith.NumberTheory.T1PhaseBudgetBound decl_use
hits_balanced_phase_of_floor_and_budget in IndisputableMonolith.NumberTheory.VisibilityFromFloorBudget decl_use

depends on (8)

Lean names referenced from this declaration's body.

cost in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4 decl_use
cost in IndisputableMonolith.Foundation.ObserverForcing decl_use
is in IndisputableMonolith.Foundation.OptionAEmpiricalProgram decl_use
is in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi decl_use
for in IndisputableMonolith.Foundation.UniversalForcingSelfReference decl_use
is in IndisputableMonolith.GameTheory.MechanismDesignFromSigma decl_use
is in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom decl_use
HitsBalancedPhase in IndisputableMonolith.NumberTheory.ErdosStrausBoxPhase decl_use