Strictly_Monotone_Real_Function_is_Bijective

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

A strictly monotone real function on an interval is injective (and hence bijective onto its image).

Why this node was retired

The posted statement is

import Mathlib.Analysis.Complex.Basic

theorem Strictly_Monotone_Real_Function_is_Bijective {f : ℝ → ℝ} {I : Set ℝ} (hf : StrictMonoOn f I) : Set.InjOn f I := by sorry

The formal conclusion is injectivity on the set, not bijectivity onto the advertised codomain.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

For a strictly monotone function f on s, conclude that f:s→f(s) is bijective. Bijectivity onto a larger specified target additionally needs surjectivity/endpoint-range hypotheses.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.