Exact expanded PA statement
forall sb sc fb fc r l. (forall gspf_index_drop_successor gspf_bit_drop_successor. (exists gsp_lt_gap_drop_successor_bound. gsp_lt_gap_drop_successor_bound + S gspf_index_drop_successor = S l) -> (((exists ff_h_gspf_drop_successor_bit. ff_h_gspf_drop_successor_bit + S (gspf_bit_drop_successor) = S ((S (gspf_index_drop_successor)) * sc)) /\ exists ff_q_gspf_drop_successor_bit. sb = ff_q_gspf_drop_successor_bit * S ((S (gspf_index_drop_successor)) * sc) + (gspf_bit_drop_successor))) -> (((gspf_bit_drop_successor = 0) /\ (((exists gsp_beta_height_gspf_drop_successor_one. gsp_beta_height_gspf_drop_successor_one + S (1) = S ((S (gspf_index_drop_successor)) * fc)) /\ exists gsp_beta_quotient_gspf_drop_successor_one. fb = gsp_beta_quotient_gspf_drop_successor_one * S ((S (gspf_index_drop_successor)) * fc) + (1)))) \/ ((gspf_bit_drop_successor = 1) /\ (((exists ff_h_gspf_drop_successor_predecessor. ff_h_gspf_drop_successor_predecessor + S (r) = S ((S (gspf_index_drop_successor)) * fc)) /\ exists ff_q_gspf_drop_successor_predecessor. fb = ff_q_gspf_drop_successor_predecessor * S ((S (gspf_index_drop_successor)) * fc) + (r)))))) -> (forall gspf_index_drop_prefix gspf_bit_drop_prefix. (exists gsp_lt_gap_drop_prefix_bound. gsp_lt_gap_drop_prefix_bound + S gspf_index_drop_prefix = l) -> (((exists ff_h_gspf_drop_prefix_bit. ff_h_gspf_drop_prefix_bit + S (gspf_bit_drop_prefix) = S ((S (gspf_index_drop_prefix)) * sc)) /\ exists ff_q_gspf_drop_prefix_bit. sb = ff_q_gspf_drop_prefix_bit * S ((S (gspf_index_drop_prefix)) * sc) + (gspf_bit_drop_prefix))) -> (((gspf_bit_drop_prefix = 0) /\ (((exists gsp_beta_height_gspf_drop_prefix_one. gsp_beta_height_gspf_drop_prefix_one + S (1) = S ((S (gspf_index_drop_prefix)) * fc)) /\ exists gsp_beta_quotient_gspf_drop_prefix_one. fb = gsp_beta_quotient_gspf_drop_prefix_one * S ((S (gspf_index_drop_prefix)) * fc) + (1)))) \/ ((gspf_bit_drop_prefix = 1) /\ (((exists ff_h_gspf_drop_prefix_predecessor. ff_h_gspf_drop_prefix_predecessor + S (r) = S ((S (gspf_index_drop_prefix)) * fc)) /\ exists ff_q_gspf_drop_prefix_predecessor. fb = ff_q_gspf_drop_prefix_predecessor * S ((S (gspf_index_drop_prefix)) * fc) + (r))))))Structural proof guide
Generated structural guide
Dropping the final position preserves the bit-to-sign-factor relation.
Use the direct prerequisites le_succ as previously established PA formulas.
The proof proceeds by direct introduction and elimination.
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 Alpha-v16 checked-use theorem is independently kernel-checked when replayed; it is not a Stable theorem.