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
(exists ftsc_first_small_zero ftsc_second_small_zero. (0) = ftsc_first_small_zero * ftsc_first_small_zero + ftsc_second_small_zero * ftsc_second_small_zero) /\ ((exists ftsc_first_small_one ftsc_second_small_one. (1) = ftsc_first_small_one * ftsc_first_small_one + ftsc_second_small_one * ftsc_second_small_one) /\ (exists ftsc_first_small_two ftsc_second_small_two. (2) = ftsc_first_small_two * ftsc_first_small_two + ftsc_second_small_two * ftsc_second_small_two))Constructive proof overview
Generated structural guide
The zero boundary, multiplicative unit, and exceptional prime two have explicit two-square witnesses.
The unchanged tactic script uses 0 declared prerequisites and contains 11 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
Direct 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.
01Separate the logical casesL1–1
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L1
split
02Construct an explicit witnessL2–3
03Calculate and transport equalitiesL4–4
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L4
norm_num
04Separate the logical casesL5–5
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L5
split
05Construct an explicit witnessL6–7
06Calculate and transport equalitiesL8–8
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L8
norm_num
07Construct an explicit witnessL9–10
08Calculate and transport equalitiesL11–11
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L11
norm_num