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.
Statement with defined notation
(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))Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.
Definitions used by this theorem
In the theorem statement
In local proof propositions
Exact expanded first-order 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))Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay command.
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