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
forall w x y z. w * w + (x + y + z) * (x + y + z) = (w * w + ((((x * x) + (y * y)) + (z * z)))) + ((((((x * y) + (y * x))) + (((x * z) + (z * x)))) + (((y * z) + (z * y)))))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
forall w x y z. w * w + (x + y + z) * (x + y + z) = (w * w + ((((x * x) + (y * y)) + (z * z)))) + ((((((x * y) + (y * x))) + (((x * z) + (z * x)))) + (((y * z) + (z * y)))))Proof neighborhood
Direct theorem prerequisites
FS002O four_square_euler_three_square_expansion add_assoc · Stable closedDirect 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.
Named ingredients (1)
01Fix variables and assumptionsL1–4
02Calculate and transport equalitiesL5–7
03Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
apply four_square_euler_three_square_expansion
04Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
symm
05Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
apply add_assoc