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
∀ x. ∀ y. ∀ z. PrimitivePythagorean(x,y,z) → PrimitivePythagorean(y,x,z)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 x y z. ((((x) * (x) + (y) * (y) = (z) * (z)) /\ (forall pff_divisor_source. (exists pff_left_source. (x) = pff_divisor_source * pff_left_source) -> (exists pff_right_source. (y) = pff_divisor_source * pff_right_source) -> pff_divisor_source = 1))) -> ((((y) * (y) + (x) * (x) = (z) * (z)) /\ (forall pff_divisor_swapped. (exists pff_left_swapped. (y) = pff_divisor_swapped * pff_left_swapped) -> (exists pff_right_swapped. (x) = pff_divisor_swapped * pff_right_swapped) -> pff_divisor_swapped = 1)))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.