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 + (c + a) = c + bStructural proof guide
Adding the same left summand preserves the witness-defined order.
Direct prerequisites: add_assoc, add_comm. The authored body proceeds by case analysis (1).
Proof neighborhood
Direct dependencies
Direct dependents
BT00R1 ceil_div_six_total BT00RI floor_ceil_complement_budget BT00UW primorial_interval_factor_prefix_shift BT00VG primorial_even_interval_divides_central BT00VH primorial_odd_interval_divides_middle BT00X1 six_block_window_decomposition_above_thirty_two BT00YA prime_square_tail_of_two_three_range BT00YB division_first_two_of_two_three_range BT010A two_lt_double_lower_six BT010P prime_contribution_interval_prefix_shift BT0110 no_bertrand_middle_contribution_interval_le_primorial_interval BT011Q bertrand_covering_intervalFormal 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.
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
04Calculate and transport equalitiesL7–8
05Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
apply add_assoc
06Calculate and transport equalitiesL10–11
07Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
apply add_comm
08Calculate and transport equalitiesL13–14
09Use earlier factsL15–15
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L15
apply add_assoc
10Calculate and transport equalitiesL16–17
11Use earlier factsL18–18
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L18
exact h_witness