Exact expanded PA statement
forall a b. (exists k. k + a = b) -> exists r. r + S a = S bStructural proof guide
Generated structural guide
Successor preserves the witness-defined order.
This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.
The proof proceeds by case analysis (1), equality transport (1).
Referenced ingredients
none
Proof neighborhood
Direct dependencies
none
Direct dependents
PA002Q new_value_lt_scaled_base PA002T beta_value_lt_scaled_base PA003G beta_prefix_sum_trace_exists PA003W beta_prefix_product_trace_exists PA008B prime_mul_index_map_exists_up_to PA008E prime_mul_index_map_injective PA008K prime_range_product_coprime PA008R prime_scaled_inverse_prefix_extend PA00A4 prime_inverse_index_exists PA00AH prime_inverse_prefix_fixed_cases PA00AL bounded_inverse_index_uniqueFormal 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.