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.
Exact expanded PA statement
forall n m k. n * (m + k) = n * m + n * kStructural proof guide
Generated structural guide
Multiplication distributes over addition on the right.
Use the direct prerequisites add_assoc as previously established PA formulas.
The proof proceeds by structural induction (1), certified simplification (2).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct 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_threeFormal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
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.