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CorollaryStatement: AI-adaptedProof: AI-generatedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-02
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

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A strictly convex function has at most one global minimizer

Statement

A strictly convex function on an interval has at most one global minimizer. This does not assert that a minimizer exists.

Facts & Assumptions

Given: A strictly convex f:I→Rf:I\to\mathbb R on an interval.

[L1]

Strict convexity makes the convexity inequality strict for distinct points and weights strictly between zero and one (Convex, strictly convex, concave, strictly concave, and midpoint-convex real functions on an interval).

Proof

technique · contradiction
1.1

Suppose distinct points x,y∈Ix,y\in I are both global minimizers.

assume-contraL1
2.1

Their midpoint lies in II, and [L1] gives f((x+y)/2)<(f(x)+f(y))/2=f(x)f((x+y)/2)<(f(x)+f(y))/2=f(x).

step 1.1algebra
3.1

This value is below a global minimum, a contradiction; hence there are at most one such point.

step 1.1step 2.1discharge-contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 6 results over 5 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources