Exact expanded first-order arithmetic statement
forall b c d e k. (forall jt_index_eqdropsource jt_left_eqdropsource jt_right_eqdropsource. (exists jt_gap_eqdropsourceindex. jt_gap_eqdropsourceindex+S (jt_index_eqdropsource)=(S k)) -> (((exists fs_h_jt_eqdropsourceleft. fs_h_jt_eqdropsourceleft + S (jt_left_eqdropsource) = S ((S (jt_index_eqdropsource)) * c)) /\ exists fs_q_jt_eqdropsourceleft. b = fs_q_jt_eqdropsourceleft * S ((S (jt_index_eqdropsource)) * c) + (jt_left_eqdropsource))) -> (((exists fs_h_jt_eqdropsourceright. fs_h_jt_eqdropsourceright + S (jt_right_eqdropsource) = S ((S (jt_index_eqdropsource)) * e)) /\ exists fs_q_jt_eqdropsourceright. d = fs_q_jt_eqdropsourceright * S ((S (jt_index_eqdropsource)) * e) + (jt_right_eqdropsource))) -> jt_left_eqdropsource=jt_right_eqdropsource) -> (forall jt_index_eqdroptarget jt_left_eqdroptarget jt_right_eqdroptarget. (exists jt_gap_eqdroptargetindex. jt_gap_eqdroptargetindex+S (jt_index_eqdroptarget)=(k)) -> (((exists fs_h_jt_eqdroptargetleft. fs_h_jt_eqdroptargetleft + S (jt_left_eqdroptarget) = S ((S (jt_index_eqdroptarget)) * c)) /\ exists fs_q_jt_eqdroptargetleft. b = fs_q_jt_eqdroptargetleft * S ((S (jt_index_eqdroptarget)) * c) + (jt_left_eqdroptarget))) -> (((exists fs_h_jt_eqdroptargetright. fs_h_jt_eqdroptargetright + S (jt_right_eqdroptarget) = S ((S (jt_index_eqdroptarget)) * e)) /\ exists fs_q_jt_eqdroptargetright. d = fs_q_jt_eqdroptargetright * S ((S (jt_index_eqdroptarget)) * e) + (jt_right_eqdroptarget))) -> jt_left_eqdroptarget=jt_right_eqdroptarget)Constructive proof overview
Generated structural guide
Restrict coordinate equality to the actual predecessor prefix.
The unchanged tactic script uses 1 declared prerequisite 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
le_succ Alpha theorem; checked-use authorizedDirect 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.
Read the argument
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.
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–12
Original exact command ledger · 22 lines
- 0001
intro b - 0002
intro c - 0003
intro d - 0004
intro e - 0005
intro k - 0006
intro h - 0007
intro i - 0008
intro a - 0009
intro z - 0010
intro hi - 0011
intro ha - 0012
intro hz - 0013
specialize h (i) - 0014
specialize h (a) - 0015
specialize h (z) - 0016
apply h - 0017
specialize le_succ (S i) - 0018
specialize le_succ (k) - 0019
apply le_succ - 0020
exact hi - 0021
exact ha - 0022
exact hz