Exact expanded first-order arithmetic statement
forall b c d e k B C D E j. (forall jt_index_listedtransport jt_left_listedtransport jt_right_listedtransport. (exists jt_gap_listedtransportindex. jt_gap_listedtransportindex+S (jt_index_listedtransport)=(k)) -> (((exists fs_h_jt_listedtransportleft. fs_h_jt_listedtransportleft + S (jt_left_listedtransport) = S ((S (jt_index_listedtransport)) * c)) /\ exists fs_q_jt_listedtransportleft. b = fs_q_jt_listedtransportleft * S ((S (jt_index_listedtransport)) * c) + (jt_left_listedtransport))) -> (((exists fs_h_jt_listedtransportright. fs_h_jt_listedtransportright + S (jt_right_listedtransport) = S ((S (jt_index_listedtransport)) * e)) /\ exists fs_q_jt_listedtransportright. d = fs_q_jt_listedtransportright * S ((S (jt_index_listedtransport)) * e) + (jt_right_listedtransport))) -> jt_left_listedtransport=jt_right_listedtransport) -> (exists jt_index_listedsource jt_code_listedsource jt_scale_listedsource. ((exists jt_gap_listedsourceindex. jt_gap_listedsourceindex+S (jt_index_listedsource)=(j)) /\ (((((((exists fs_h_jt_listedsourcecode. fs_h_jt_listedsourcecode + S (jt_code_listedsource) = S ((S (jt_index_listedsource)) * C)) /\ exists fs_q_jt_listedsourcecode. B = fs_q_jt_listedsourcecode * S ((S (jt_index_listedsource)) * C) + (jt_code_listedsource))) /\ (((exists fs_h_jt_listedsourcescale. fs_h_jt_listedsourcescale + S (jt_scale_listedsource) = S ((S (jt_index_listedsource)) * E)) /\ exists fs_q_jt_listedsourcescale. D = fs_q_jt_listedsourcescale * S ((S (jt_index_listedsource)) * E) + (jt_scale_listedsource))))) /\ (forall jt_index_listedsourceequal jt_left_listedsourceequal jt_right_listedsourceequal. (exists jt_gap_listedsourceequalindex. jt_gap_listedsourceequalindex+S (jt_index_listedsourceequal)=(k)) -> (((exists fs_h_jt_listedsourceequalleft. fs_h_jt_listedsourceequalleft + S (jt_left_listedsourceequal) = S ((S (jt_index_listedsourceequal)) * e)) /\ exists fs_q_jt_listedsourceequalleft. d = fs_q_jt_listedsourceequalleft * S ((S (jt_index_listedsourceequal)) * e) + (jt_left_listedsourceequal))) -> (((exists fs_h_jt_listedsourceequalright. fs_h_jt_listedsourceequalright + S (jt_right_listedsourceequal) = S ((S (jt_index_listedsourceequal)) * jt_scale_listedsource)) /\ exists fs_q_jt_listedsourceequalright. jt_code_listedsource = fs_q_jt_listedsourceequalright * S ((S (jt_index_listedsourceequal)) * jt_scale_listedsource) + (jt_right_listedsourceequal))) -> jt_left_listedsourceequal=jt_right_listedsourceequal))))) -> (exists jt_index_listedtarget jt_code_listedtarget jt_scale_listedtarget. ((exists jt_gap_listedtargetindex. jt_gap_listedtargetindex+S (jt_index_listedtarget)=(j)) /\ (((((((exists fs_h_jt_listedtargetcode. fs_h_jt_listedtargetcode + S (jt_code_listedtarget) = S ((S (jt_index_listedtarget)) * C)) /\ exists fs_q_jt_listedtargetcode. B = fs_q_jt_listedtargetcode * S ((S (jt_index_listedtarget)) * C) + (jt_code_listedtarget))) /\ (((exists fs_h_jt_listedtargetscale. fs_h_jt_listedtargetscale + S (jt_scale_listedtarget) = S ((S (jt_index_listedtarget)) * E)) /\ exists fs_q_jt_listedtargetscale. D = fs_q_jt_listedtargetscale * S ((S (jt_index_listedtarget)) * E) + (jt_scale_listedtarget))))) /\ (forall jt_index_listedtargetequal jt_left_listedtargetequal jt_right_listedtargetequal. (exists jt_gap_listedtargetequalindex. jt_gap_listedtargetequalindex+S (jt_index_listedtargetequal)=(k)) -> (((exists fs_h_jt_listedtargetequalleft. fs_h_jt_listedtargetequalleft + S (jt_left_listedtargetequal) = S ((S (jt_index_listedtargetequal)) * c)) /\ exists fs_q_jt_listedtargetequalleft. b = fs_q_jt_listedtargetequalleft * S ((S (jt_index_listedtargetequal)) * c) + (jt_left_listedtargetequal))) -> (((exists fs_h_jt_listedtargetequalright. fs_h_jt_listedtargetequalright + S (jt_right_listedtargetequal) = S ((S (jt_index_listedtargetequal)) * jt_scale_listedtarget)) /\ exists fs_q_jt_listedtargetequalright. jt_code_listedtarget = fs_q_jt_listedtargetequalright * S ((S (jt_index_listedtargetequal)) * jt_scale_listedtarget) + (jt_right_listedtargetequal))) -> jt_left_listedtargetequal=jt_right_listedtargetequal)))))Constructive proof overview
Generated structural guide
List membership is a property of the represented coordinate tuple.
The unchanged tactic script uses 1 declared prerequisite and contains 34 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.
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.
Named ingredients (1)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–12
03Separate the logical casesL13–17
04Construct an explicit witnessL18–20
05Separate the logical casesL21–21
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L21
split
06Use earlier factsL22–22
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L22
exact hl_witness_witness_witness_left
07Separate the logical casesL23–23
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L23
split
08Use earlier factsL24–33
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L24
exact hl_witness_witness_witness_right_left - L25
specialize jordan_tuple_equal_trans (b) - L26
specialize jordan_tuple_equal_trans (c) - L27
specialize jordan_tuple_equal_trans (d) - L28
specialize jordan_tuple_equal_trans (e) - L29
specialize jordan_tuple_equal_trans (x1) - L30
specialize jordan_tuple_equal_trans (x2) - L31
specialize jordan_tuple_equal_trans (k) - L32
apply jordan_tuple_equal_trans - L33
exact heq
09Use earlier factsL34–34
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L34
exact hl_witness_witness_witness_right_right
Original exact command ledger · 34 lines
- 0001
intro b - 0002
intro c - 0003
intro d - 0004
intro e - 0005
intro k - 0006
intro B - 0007
intro C - 0008
intro D - 0009
intro E - 0010
intro j - 0011
intro heq - 0012
intro hl - 0013
cases hl - 0014
cases hl_witness - 0015
cases hl_witness_witness - 0016
cases hl_witness_witness_witness - 0017
cases hl_witness_witness_witness_right - 0018
exists x - 0019
exists x1 - 0020
exists x2 - 0021
split - 0022
exact hl_witness_witness_witness_left - 0023
split - 0024
exact hl_witness_witness_witness_right_left - 0025
specialize jordan_tuple_equal_trans (b) - 0026
specialize jordan_tuple_equal_trans (c) - 0027
specialize jordan_tuple_equal_trans (d) - 0028
specialize jordan_tuple_equal_trans (e) - 0029
specialize jordan_tuple_equal_trans (x1) - 0030
specialize jordan_tuple_equal_trans (x2) - 0031
specialize jordan_tuple_equal_trans (k) - 0032
apply jordan_tuple_equal_trans - 0033
exact heq - 0034
exact hl_witness_witness_witness_right_right