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 rc ic a b c d. ((((rc) = 2 * (a) /\ (b) = 0) \/ exists ge_signed_half_from_signed_real. (((rc) = 2 * ge_signed_half_from_signed_real + 1 /\ (a) = 0) /\ (b) = S ge_signed_half_from_signed_real))) -> ((((ic) = 2 * (c) /\ (d) = 0) \/ exists ge_signed_half_from_signed_imaginary. (((ic) = 2 * ge_signed_half_from_signed_imaginary + 1 /\ (c) = 0) /\ (d) = S ge_signed_half_from_signed_imaginary))) -> exists z. (exists ge_real_code_from_signed_codes ge_imaginary_code_from_signed_codes. (((z) = ((ge_real_code_from_signed_codes) + (ge_imaginary_code_from_signed_codes)) * S ((ge_real_code_from_signed_codes) + (ge_imaginary_code_from_signed_codes)) + ((ge_imaginary_code_from_signed_codes) + (ge_imaginary_code_from_signed_codes))) /\ (((((ge_real_code_from_signed_codes) = 2 * (a) /\ (b) = 0) \/ exists ge_signed_half_ge_from_signed_codes_real. (((ge_real_code_from_signed_codes) = 2 * ge_signed_half_ge_from_signed_codes_real + 1 /\ (a) = 0) /\ (b) = S ge_signed_half_ge_from_signed_codes_real))) /\ ((((ge_imaginary_code_from_signed_codes) = 2 * (c) /\ (d) = 0) \/ exists ge_signed_half_ge_from_signed_codes_imaginary. (((ge_imaginary_code_from_signed_codes) = 2 * ge_signed_half_ge_from_signed_codes_imaginary + 1 /\ (c) = 0) /\ (d) = S ge_signed_half_ge_from_signed_codes_imaginary))))))Constructive proof overview
Generated structural guide
Pair two actual normalized signed-integer codes into their genuine canonical natural Gaussian coordinate code.
The unchanged tactic script uses 0 declared prerequisites and contains 16 exact native proof lines.
Alpha v34 checked-use · first admitted v28 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct 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.
01Fix variables and assumptionsL1–8
02Construct an explicit witnessL9–11
03Separate the logical casesL12–12
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L12
split
04Calculate and transport equalitiesL13–13
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L13
refl
05Separate the logical casesL14–14
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L14
split