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
∀ m. ∀ a. ModEq(m,a,a)Every purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall m a. exists u v. a + m * u = a + m * vProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
PA0026 binary_crt PA003Q coprime_mod_inverse PA005E pow_predecessor_parity_mod PA005I pow_mod_congruent PA007Q beta_product_pointwise_scale_mod PA00A0 beta_adjacent_target_pairs_product_power PA00AO inverse_prefix_zero_fixed PA00B9 beta_adjacent_unit_pairs_product_one PA00BJ prime_factorial_wilson_congruence PA00CM signed_remainder_sum_mod_twoDefinition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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 assumptionsL1–2
02Construct an explicit witnessL3–4
03Calculate and transport equalitiesL5–5
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L5
refl