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 + a = b) -> exists r. r + a * c = b * cStructural proof guide
Right multiplication preserves the witness-defined order.
Direct prerequisites: add_mul. The authored body proceeds by case analysis (1).
Proof neighborhood
Direct dependencies
Direct dependents
BT0055 le_scaled_nonzero BT00PV mul_le_mul BT00PX le_mul_of_one_le_left BT00R9 square_lt_successor_square BT00RC floor_sqrt_monotone BT00RG double_triple_remainder_complement_budget BT00TY mul_lt_mul_right_nonzero BT00VK central_binom_strong_upper_step BT00X6 bertrand_main_inequality_factorized_from_total BT00YH floor_sqrt_above_root_power_two_strict BT010C three_mul_le_square_of_three_le BT0117 factor_pair_has_small_member_below_squareFormal 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.
Named ingredients (1)
01Fix variables and assumptionsL1–4
02Separate the logical casesL5–5
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L5
cases h
03Construct an explicit witnessL6–6
Supply the displayed value, then prove that it has the required property.
- L6
exists x * c
04Calculate and transport equalitiesL7–8
05Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
apply add_mul
06Calculate and transport equalitiesL10–10
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L10
congr
07Use earlier factsL11–11
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L11
exact h_witness
08Calculate and transport equalitiesL12–12
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L12
refl