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 expanded first-order arithmetic statement
exists mps_positive_unit_negation mps_negative_unit_negation. (((((2) = 2 * (mps_positive_unit_negation) /\ (mps_negative_unit_negation) = 0) \/ exists ge_signed_half_unit_negationsource. (((2) = 2 * ge_signed_half_unit_negationsource + 1 /\ (mps_positive_unit_negation) = 0) /\ (mps_negative_unit_negation) = S ge_signed_half_unit_negationsource))) /\ ((((1) = 2 * (mps_negative_unit_negation) /\ (mps_positive_unit_negation) = 0) \/ exists ge_signed_half_unit_negationtarget. (((1) = 2 * ge_signed_half_unit_negationtarget + 1 /\ (mps_negative_unit_negation) = 0) /\ (mps_positive_unit_negation) = S ge_signed_half_unit_negationtarget))))Constructive proof overview
Generated structural guide
Canonical code two is positive one and code one is its genuine decoded additive inverse.
The unchanged tactic script uses 2 declared prerequisites and contains 17 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
mul_one Stable theorem; checked-use authorized zero_add 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 exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply 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.
01Construct an explicit witnessL1–2
02Separate the logical casesL3–5
03Calculate and transport equalitiesL6–6
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L6
symm
04Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
apply mul_one
05Calculate and transport equalitiesL8–8
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L8
refl
06Separate the logical casesL9–9
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L9
right
07Construct an explicit witnessL10–10
Supply the displayed value, then prove that it has the required property.
- L10
exists 0
08Separate the logical casesL11–12
09Calculate and transport equalitiesL13–14
10Use earlier factsL15–15
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L15
apply zero_add