ExampleConstruction: AI-adaptedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-01

How statement and proof provenance work

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.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Kruskal's and Prim's procedures on the same weighted graph

Statement

Let $G$ have edges $ab,bc,cd,ad,ac$ of weights $1,2,3,4,5$ , respectively. Kruskal's procedure chooses $ab,bc,cd$ . Prim's procedure started at $a$ makes the same choices, and the resulting MST has total weight $6$ .

Facts & Assumptions

Given: The weighted graph $(G,w)$ above.

[L1]

Kruskal adds the lightest edge that does not form a cycle (Kruskal's greedy edge procedure produces a minimum spanning tree).

[L2]

Prim adds the lightest edge leaving the reached set (Prim's growing-tree procedure produces a minimum spanning tree).

[F1]

Tree weight is the sum of its edge weights (Real edge-weighted graphs, total tree weight and minimum spanning trees).

Verification

technique · direct computation

1.1

Kruskal considers the edges in weight order and accepts $ab$ , then $bc$ , then $cd$ ; at that point all four vertices are connected.

1.2

From $a$ , Prim first chooses $ab$ of weight $1$ , then $bc$ of weight $2$ , then $cd$ of weight $3$ .

2.1

Both procedures output the path with total weight $1+2+3=6$ , and their correctness theorems make it an MST.

step 1.1step 1.2F1L1L2∎

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: 49 results over 19 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

ISI Bangalore discrete mathematics notes, Kruskal and other algorithms (standard reference, not scraped)