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
∀ m. ∀ n. Coprime(m · m,n · n) → Coprime(m,n)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 m n. (forall pff_divisor_pi_root_source. (exists pff_left_pi_root_source. (m * m) = pff_divisor_pi_root_source * pff_left_pi_root_source) -> (exists pff_right_pi_root_source. (n * n) = pff_divisor_pi_root_source * pff_right_pi_root_source) -> pff_divisor_pi_root_source = 1) -> (forall pff_divisor_pi_root_result. (exists pff_left_pi_root_result. (m) = pff_divisor_pi_root_result * pff_left_pi_root_result) -> (exists pff_right_pi_root_result. (n) = pff_divisor_pi_root_result * pff_right_pi_root_result) -> pff_divisor_pi_root_result = 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.