PA003V

succ_injective

Stable checked-use theorem · independently closed

Successor is injective (the reusable PA2 lemma).

Exact expanded PA statement

forall n m. S n = S m -> n = m

Structural proof guide

Generated structural guide

Successor is injective (the reusable PA2 lemma).

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

PA007D beta_magnitude_predecessor_recode_exists PA008E prime_mul_index_map_injective PA009M beta_prefix_append_two_scaled_orbit_closed PA00AE finite_prefix_choose_unused_nonendpoint PA00AG prime_bounded_square_one_cases PA00AH prime_inverse_prefix_fixed_cases PA00AL bounded_inverse_index_unique PA00AQ prime_inverse_prefix_nonendpoint_mate PA00BJ prime_factorial_wilson_congruence

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. 0001apply PA2