Exact expanded PA statement
forall b c n sn. sn = S n -> (forall fp_i_bounded_succ. (exists fp_gap_bounded_succ_index. fp_gap_bounded_succ_index + S fp_i_bounded_succ = sn) -> exists fp_value_bounded_succ. ((((exists ff_h_bounded_succ_entry. ff_h_bounded_succ_entry + S (fp_value_bounded_succ) = S ((S (fp_i_bounded_succ)) * c)) /\ exists ff_q_bounded_succ_entry. b = ff_q_bounded_succ_entry * S ((S (fp_i_bounded_succ)) * c) + (fp_value_bounded_succ))) /\ (exists fp_gap_bounded_succ_value. fp_gap_bounded_succ_value + S fp_value_bounded_succ = sn))) -> exists x. ((((exists ff_h_last_x. ff_h_last_x + S (x) = S ((S (n)) * c)) /\ exists ff_q_last_x. b = ff_q_last_x * S ((S (n)) * c) + (x))) /\ exists h. h + S x = S n)Structural proof guide
Generated structural guide
A bounded successor prefix exposes a bounded final decoded value.
Use the direct prerequisites le_refl as previously established PA formulas.
The proof proceeds by equality transport (2).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
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.