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Foundation /
Foundation.VariationalDynamics /
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formal statement (Lean)
403 theorem trajectory_defect_monotone {N : ℕ}
404 (traj : Trajectory N)
405 (h : IsVariationalTrajectory traj) :
406 ∀ t, total_defect (traj (t + 1)) ≤ total_defect (traj t) :=
proof body
Term-mode proof.
407 fun t => variational_step_reduces_defect (traj t) (traj (t + 1)) (h t)
408
409 /-! ## Global Consistency: Non-Locality of the Update -/
410
411 /-- **Structure (Localized Update)**: An update that modifies only one entry,
412 holding all others fixed. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (19)
Lean names referenced from this declaration's body.
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