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.
The derivative-nonzero criterion supplies no inverse or power witness: both are constructed. Roots may be arbitrary natural representatives of signed integer polynomials. Singular-root classification and p-adic completion are separate milestones.
Exact theorem in conservative defined notation
∀ h. ∀ A. ∀ B. A + h · B + B = A + S h · BEvery linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 14 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
01Fix variables and assumptionsL1–3
02Calculate and transport equalitiesL4–4
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L4
trans A + (h * B + B)
03Use earlier factsL5–5
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L5
apply add_assoc
04Calculate and transport equalitiesL6–9
05Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
apply mul_comm
06Calculate and transport equalitiesL11–12
07Use earlier factsL13–13
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L13
apply mul_comm
08Calculate and transport equalitiesL14–14
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L14
refl