Exact expanded first-order arithmetic statement
forall b c d e k. (forall jt_index_symmsource jt_left_symmsource jt_right_symmsource. (exists jt_gap_symmsourceindex. jt_gap_symmsourceindex+S (jt_index_symmsource)=(k)) -> (((exists fs_h_jt_symmsourceleft. fs_h_jt_symmsourceleft + S (jt_left_symmsource) = S ((S (jt_index_symmsource)) * c)) /\ exists fs_q_jt_symmsourceleft. b = fs_q_jt_symmsourceleft * S ((S (jt_index_symmsource)) * c) + (jt_left_symmsource))) -> (((exists fs_h_jt_symmsourceright. fs_h_jt_symmsourceright + S (jt_right_symmsource) = S ((S (jt_index_symmsource)) * e)) /\ exists fs_q_jt_symmsourceright. d = fs_q_jt_symmsourceright * S ((S (jt_index_symmsource)) * e) + (jt_right_symmsource))) -> jt_left_symmsource=jt_right_symmsource) -> (forall jt_index_symmtarget jt_left_symmtarget jt_right_symmtarget. (exists jt_gap_symmtargetindex. jt_gap_symmtargetindex+S (jt_index_symmtarget)=(k)) -> (((exists fs_h_jt_symmtargetleft. fs_h_jt_symmtargetleft + S (jt_left_symmtarget) = S ((S (jt_index_symmtarget)) * e)) /\ exists fs_q_jt_symmtargetleft. d = fs_q_jt_symmtargetleft * S ((S (jt_index_symmtarget)) * e) + (jt_left_symmtarget))) -> (((exists fs_h_jt_symmtargetright. fs_h_jt_symmtargetright + S (jt_right_symmtarget) = S ((S (jt_index_symmtarget)) * c)) /\ exists fs_q_jt_symmtargetright. b = fs_q_jt_symmtargetright * S ((S (jt_index_symmtarget)) * c) + (jt_right_symmtarget))) -> jt_left_symmtarget=jt_right_symmtarget)Constructive proof overview
Generated structural guide
Coordinate equality is symmetric without selecting canonical codes.
The unchanged tactic script uses 0 declared prerequisites and contains 22 exact native proof lines.
Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
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Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.