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.
Exact expanded first-order arithmetic statement
forall h. exists e. (((h = 2 * e) \/ (exists qst_count_half_shape. h = 2 * qst_count_half_shape + 1 /\ e = S qst_count_half_shape)))Constructive proof overview
Generated structural guide
The explicit reflection-count shape for doubling exists constructively for every odd-prime half.
The unchanged tactic script uses 1 declared prerequisite and contains 13 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
parity_cases Stable theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This dependency-curried candidate body does not grant checked theorem use or Stable membership.
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 assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro h
02Use earlier factsL2–2
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L2
specialize parity_cases h
03Separate the logical casesL3–4
04Construct an explicit witnessL5–5
Supply the displayed value, then prove that it has the required property.
- L5
exists x
05Separate the logical casesL6–6
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L6
left
06Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
exact parity_cases_witness_left
07Construct an explicit witnessL8–8
Supply the displayed value, then prove that it has the required property.
- L8
exists S x
08Separate the logical casesL9–9
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L9
right
09Construct an explicit witnessL10–10
Supply the displayed value, then prove that it has the required property.
- L10
exists x
10Separate the logical casesL11–11
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L11
split
11Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
exact parity_cases_witness_right
12Calculate and transport equalitiesL13–13
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L13
refl