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 a b c. (exists k. k + S a = b) -> (exists k. k + b = c) -> exists k. k + S a = cStructural proof guide
Strict order followed by weak order remains strict.
Direct prerequisites: le_trans. The authored body proceeds by direct introduction and elimination.
Proof neighborhood
Direct dependencies
Direct dependents
BT003K prime_divisor_exists_up_to BT00R2 ceil_div_six_functional BT00RC floor_sqrt_monotone BT00RF ceil_div_six_le_of_upper BT00TY mul_lt_mul_right_nonzero BT00UX primorial_factor_prefix_restrict_add BT00XK pow_tail_strict_of_square BT00XO prime_power_quotient_zero_of_exponent_gt BT00YA prime_square_tail_of_two_three_range BT00YF division_three_scaled_upper_of_quotient_lt BT00YH floor_sqrt_above_root_power_two_strict BT010B floor_sqrt_two_le_of_two_lt BT010E division_quotient_lower_of_scaled_le BT010Q prime_contribution_prefix_restrict_add BT0115 bertrand_eventually_closed_upperFormal native tactic body
Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.
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.