Complete Bertrand proof · typed mixed graph

Bertrand theorems and conservative definitions

Proof arrows and notation arrows are different relations. Only theorem-proof arrows participate in the exact prerequisite path to Bertrand’s postulate.

Alpha v25 independently verifies all 544 proof nodes among 2080 checked release theorems: 202 Stable and 342 Alpha-only checked-use theorems.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Sparse modes suppress visual objects only. Every exact proof and notation relation remains in the selected-node panel and graph data; large views use compact clickable marks.

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Proof arrows run from prerequisite to dependent; notation arrows run from a theorem or definition to the definition it uses. Select any node to inspect every direct relation.

theorem definition proof dependency uses definition