One_Parameter_Family_of_Curves_for_First_Order_ODE
Proved⚠️ Retired — incorrect formalization
The Lean statement below asserts nothing: its conclusion is the proposition
True, which is closed bytrivialin any context. Its proof status therefore records no mathematical content and says nothing aboutOne_Parameter_Family_of_Curves_for_First_Order_ODE. Do not import it or use it as a dependency.
Every one-parameter family of curves is the general solution of some first order ODE, and conversely.
Why this node was retired
The posted statement is
theorem One_Parameter_Family_of_Curves_for_First_Order_ODE (F : ℝ → ℝ → ℝ → Prop) (c : ℝ) : True := by sorry
and its goal is True. Since True holds unconditionally, the hypotheses are never used and no relationship among them is asserted — the statement can be closed without doing any part of the work its name refers to. Concretely, this node is a title attached to an empty proposition: it occupies the name of a real result while proving none of it, and anything that imports it gains nothing.
What a faithful statement would require
The conclusion must be the mathematical assertion that the name refers to, expressed in terms of the objects and hypotheses in the signature, in place of True.
No corrected replacement node exists yet.
import Mathlib.Analysis.Complex.Basic
theorem One_Parameter_Family_of_Curves_for_First_Order_ODE (F : ℝ → ℝ → ℝ → Prop) (c : ℝ) : True := by sorry