Exact expanded first-order arithmetic statement
forall m n b c d e f g. forall jt_index_crtempty. (exists jt_gap_crtemptyindex. jt_gap_crtemptyindex+S (jt_index_crtempty)=(0)) -> exists jt_left_crtempty jt_right_crtempty jt_output_crtempty. ((((exists fs_h_jt_crtemptyleft. fs_h_jt_crtemptyleft + S (jt_left_crtempty) = S ((S (jt_index_crtempty)) * c)) /\ exists fs_q_jt_crtemptyleft. b = fs_q_jt_crtemptyleft * S ((S (jt_index_crtempty)) * c) + (jt_left_crtempty))) /\ (((((exists fs_h_jt_crtemptyright. fs_h_jt_crtemptyright + S (jt_right_crtempty) = S ((S (jt_index_crtempty)) * e)) /\ exists fs_q_jt_crtemptyright. d = fs_q_jt_crtemptyright * S ((S (jt_index_crtempty)) * e) + (jt_right_crtempty))) /\ (((((exists fs_h_jt_crtemptyoutput. fs_h_jt_crtemptyoutput + S (jt_output_crtempty) = S ((S (jt_index_crtempty)) * g)) /\ exists fs_q_jt_crtemptyoutput. f = fs_q_jt_crtemptyoutput * S ((S (jt_index_crtempty)) * g) + (jt_output_crtempty))) /\ (((exists jt_left_crtemptymodleft jt_right_crtemptymodleft. (jt_output_crtempty)+(m)*jt_left_crtemptymodleft=(jt_left_crtempty)+(m)*jt_right_crtemptymodleft) /\ (exists jt_left_crtemptymodright jt_right_crtemptymodright. (jt_output_crtempty)+(n)*jt_left_crtemptymodright=(jt_right_crtempty)+(n)*jt_right_crtemptymodright))))))))Constructive proof overview
Generated structural guide
The empty simultaneous coordinate congruence has no missing witness.
The unchanged tactic script uses 2 declared prerequisites and contains 17 exact native proof lines.
Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_not_le Alpha theorem; checked-use authorized zero_le 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
02Separate the logical casesL11–11
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L11
exfalso