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
∀ a. ∀ b. Le(a,a + b)Every purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
Definitions used by this theorem
In the theorem statement
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall a b. exists k. k + a = a + bProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT0057 beta_value_lt_scaled_base BT00RG double_triple_remainder_complement_budget BT00UX primorial_factor_prefix_restrict_add BT00VV primorial_le_four_pow_bounded BT00X1 six_block_window_decomposition_above_thirty_two BT00X2 bertrand_hj_six_block_iterate_from_total BT00X4 bertrand_floor_power_product_le_h_from_total BT00Y5 central_binom_prime_power_contribution_le_double BT010H division_quotient_le_dividend BT010Q prime_contribution_prefix_restrict_add BT010V no_bertrand_small_contribution_choice_le_doubleDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
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.