PA0023

mod_eq_refl

Stable checked-use theorem · independently closed

Balanced natural congruence is reflexive.

Exact expanded PA statement

forall m a. exists u v. a + m * u = a + m * v

Structural proof guide

Generated structural guide

Balanced natural congruence is reflexive.

This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.

The proof proceeds by direct introduction and elimination.

Referenced ingredients

none

Proof neighborhood

Direct dependencies

none

Direct 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_two

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.

  1. 0001intro m
  2. 0002intro a
  3. 0003exists 0
  4. 0004exists 0
  5. 0005refl