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. Coprime(x,y) → Coprime(y,x)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. (forall pff_divisor_swap_forward. (exists pff_left_swap_forward. (x) = pff_divisor_swap_forward * pff_left_swap_forward) -> (exists pff_right_swap_forward. (y) = pff_divisor_swap_forward * pff_right_swap_forward) -> pff_divisor_swap_forward = 1) -> (forall pff_divisor_swap_backward. (exists pff_left_swap_backward. (y) = pff_divisor_swap_backward * pff_left_swap_backward) -> (exists pff_right_swap_backward. (x) = pff_divisor_swap_backward * pff_right_swap_backward) -> pff_divisor_swap_backward = 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.