Alphabeta MathTheoremStatement: AI-adaptedProof: AI-adaptedprecheck passaudited 2026-08-02
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.
The complex exponential maps onto
Statement
The complex exponential maps onto . The conventions and prerequisite facts used below are recorded in Every nonzero complex number has a unique polar form with and , , , and , The natural logarithm as the inverse of the exponential function, Order, continuity, range, and the product, quotient, and reciprocal laws for the natural logarithm.
Facts & Assumptions
Given: .
Proof
technique · constructive
1.1given
Write with .
1.2construct
Put .
2.1discharge-construct∎
Cartesian exponential form and give .