Exact expanded first-order arithmetic statement
forall b c d e k. (forall jt_index_unit_left. (exists jt_gap_unit_leftindex. jt_gap_unit_leftindex+S (jt_index_unit_left)=(k)) -> exists jt_value_unit_left. ((((exists fs_h_jt_unit_leftat. fs_h_jt_unit_leftat + S (jt_value_unit_left) = S ((S (jt_index_unit_left)) * c)) /\ exists fs_q_jt_unit_leftat. b = fs_q_jt_unit_leftat * S ((S (jt_index_unit_left)) * c) + (jt_value_unit_left))) /\ (exists jt_gap_unit_leftvalue. jt_gap_unit_leftvalue+S (jt_value_unit_left)=(1)))) -> (forall jt_index_unit_right. (exists jt_gap_unit_rightindex. jt_gap_unit_rightindex+S (jt_index_unit_right)=(k)) -> exists jt_value_unit_right. ((((exists fs_h_jt_unit_rightat. fs_h_jt_unit_rightat + S (jt_value_unit_right) = S ((S (jt_index_unit_right)) * e)) /\ exists fs_q_jt_unit_rightat. d = fs_q_jt_unit_rightat * S ((S (jt_index_unit_right)) * e) + (jt_value_unit_right))) /\ (exists jt_gap_unit_rightvalue. jt_gap_unit_rightvalue+S (jt_value_unit_right)=(1)))) -> (forall jt_index_unit_equal jt_left_unit_equal jt_right_unit_equal. (exists jt_gap_unit_equalindex. jt_gap_unit_equalindex+S (jt_index_unit_equal)=(k)) -> (((exists fs_h_jt_unit_equalleft. fs_h_jt_unit_equalleft + S (jt_left_unit_equal) = S ((S (jt_index_unit_equal)) * c)) /\ exists fs_q_jt_unit_equalleft. b = fs_q_jt_unit_equalleft * S ((S (jt_index_unit_equal)) * c) + (jt_left_unit_equal))) -> (((exists fs_h_jt_unit_equalright. fs_h_jt_unit_equalright + S (jt_right_unit_equal) = S ((S (jt_index_unit_equal)) * e)) /\ exists fs_q_jt_unit_equalright. d = fs_q_jt_unit_equalright * S ((S (jt_index_unit_equal)) * e) + (jt_right_unit_equal))) -> jt_left_unit_equal=jt_right_unit_equal)Constructive proof overview
Generated structural guide
Any two canonical tuples modulo one represent the same coordinate tuple.
The unchanged tactic script uses 1 declared prerequisite and contains 23 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 assumptionsL11–13
03Calculate and transport equalitiesL14–14
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L14
trans 0
04Use earlier factsL15–18
05Calculate and transport equalitiesL19–19
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L19
symm
Original exact command ledger · 23 lines
- 0001
intro b - 0002
intro c - 0003
intro d - 0004
intro e - 0005
intro k - 0006
intro hLeft - 0007
intro hRight - 0008
intro i - 0009
intro a - 0010
intro z - 0011
intro hi - 0012
intro ha - 0013
intro hz - 0014
trans 0 - 0015
apply jordan_tuple_bounded_one_entry_zero - 0016
exact hLeft - 0017
exact hi - 0018
exact ha - 0019
symm - 0020
apply jordan_tuple_bounded_one_entry_zero - 0021
exact hRight - 0022
exact hi - 0023
exact hz