def
definition
def or abbrev
ode_regularity_differentiable_hypothesis
show as:
view Lean formalization →
formal statement (Lean)
474def ode_regularity_differentiable_hypothesis (H : ℝ → ℝ) : Prop :=
proof body
Definition body.
475 (∀ t, deriv (deriv H) t = H t) → Continuous H → Differentiable ℝ H
476
477/-! ### Proving the regularity hypotheses
478
479For the linear ODE f'' = f, we can verify the regularity hypotheses hold
480for the known solution cosh. For arbitrary solutions, we rely on general
481ODE theory (Picard-Lindelöf). -/
482
483/-- cosh satisfies the ODE regularity bootstrap. -/
used by (16)
-
cost_algebra_unique -
cosh_satisfies_differentiable -
dAlembert_cosh_solution -
dAlembert_cosh_solution_of_log_curvature -
ode_cosh_uniqueness -
ode_regularity_continuous_of_smooth -
ode_regularity_differentiable_of_smooth -
washburn_uniqueness -
ode_regularity_continuous_of_smooth -
ode_regularity_differentiable_of_smooth -
T5_uniqueness_complete -
UniqueCostAxioms -
unique_cost_on_pos_from_rcl -
uniqueness_specification -
dAlembert_classification -
ZeroCompositionLaw