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 n m k. n * (m + k) = n * m + n * kEvery purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall n m k. n * (m + k) = n * m + n * kProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA000B mul_assoc PA0016 add_mul PA001G divides_linear_step PA001J balanced_bezout_euclid_step PA001O common_divisor_divides_balanced_result PA0022 mod_eq_add PA0024 mod_eq_trans PA0026 binary_crt PA002D positive_quotient_gap_impossible PA003Q coprime_mod_inverse PA005N square_decomp PA005O add_residue PA006D odd_mul_odd PA006F even_add_odd PA006G odd_add_even PA006H even_add_even PA006I odd_add_odd PA006M mul_le_mul_left PA007B gauss_mixed_sign_scaled_source_impossible PA00DQ odd_half_cross_product_gap PA00FQ odd_half_of_mod4_three_exact PA00FR odd_half_odd_iff_mod4_threeDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed 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.