Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall A r s i j a. (exists dst_positive_code_hit_source dst_positive_scale_hit_source dst_negative_code_hit_source dst_negative_scale_hit_source dst_positive_hit_source dst_negative_hit_source. (((A) = (((((dst_positive_code_hit_source) + (dst_positive_scale_hit_source)) * S ((dst_positive_code_hit_source) + (dst_positive_scale_hit_source)) + ((dst_positive_scale_hit_source) + (dst_positive_scale_hit_source))) + (((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) * S ((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) + ((dst_negative_scale_hit_source) + (dst_negative_scale_hit_source)))) * S ((((dst_positive_code_hit_source) + (dst_positive_scale_hit_source)) * S ((dst_positive_code_hit_source) + (dst_positive_scale_hit_source)) + ((dst_positive_scale_hit_source) + (dst_positive_scale_hit_source))) + (((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) * S ((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) + ((dst_negative_scale_hit_source) + (dst_negative_scale_hit_source)))) + ((((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) * S ((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) + ((dst_negative_scale_hit_source) + (dst_negative_scale_hit_source))) + (((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) * S ((dst_negative_code_hit_source) + (dst_negative_scale_hit_source)) + ((dst_negative_scale_hit_source) + (dst_negative_scale_hit_source)))))) /\ (((((exists ff_h_pvs_hit_sourcepositive. ff_h_pvs_hit_sourcepositive + S (dst_positive_hit_source) = S ((S (i)) * dst_positive_scale_hit_source)) /\ exists ff_q_pvs_hit_sourcepositive. dst_positive_code_hit_source = ff_q_pvs_hit_sourcepositive * S ((S (i)) * dst_positive_scale_hit_source) + (dst_positive_hit_source))) /\ (((((exists ff_h_pvs_hit_sourcenegative. ff_h_pvs_hit_sourcenegative + S (dst_negative_hit_source) = S ((S (i)) * dst_negative_scale_hit_source)) /\ exists ff_q_pvs_hit_sourcenegative. dst_negative_code_hit_source = ff_q_pvs_hit_sourcenegative * S ((S (i)) * dst_negative_scale_hit_source) + (dst_negative_hit_source))) /\ (exists ge_balance_positive_hit_sourcevalue ge_balance_negative_hit_sourcevalue. (((((a) = 2 * (ge_balance_positive_hit_sourcevalue) /\ (ge_balance_negative_hit_sourcevalue) = 0) \/ exists ge_signed_half_hit_sourcevaluedecode. (((a) = 2 * ge_signed_half_hit_sourcevaluedecode + 1 /\ (ge_balance_positive_hit_sourcevalue) = 0) /\ (ge_balance_negative_hit_sourcevalue) = S ge_signed_half_hit_sourcevaluedecode))) /\ ((dst_positive_hit_source) + ge_balance_negative_hit_sourcevalue = (dst_negative_hit_source) + ge_balance_positive_hit_sourcevalue))))))))) -> (((exists ff_h_pvs_hit_map. ff_h_pvs_hit_map + S (j) = S ((S (i)) * s)) /\ exists ff_q_pvs_hit_map. r = ff_q_pvs_hit_map * S ((S (i)) * s) + (j))) -> (exists ssr_entry_value_hit_entry ssr_entry_image_hit_entry. ((exists dst_positive_code_hit_entrysource dst_positive_scale_hit_entrysource dst_negative_code_hit_entrysource dst_negative_scale_hit_entrysource dst_positive_hit_entrysource dst_negative_hit_entrysource. (((A) = (((((dst_positive_code_hit_entrysource) + (dst_positive_scale_hit_entrysource)) * S ((dst_positive_code_hit_entrysource) + (dst_positive_scale_hit_entrysource)) + ((dst_positive_scale_hit_entrysource) + (dst_positive_scale_hit_entrysource))) + (((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) * S ((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) + ((dst_negative_scale_hit_entrysource) + (dst_negative_scale_hit_entrysource)))) * S ((((dst_positive_code_hit_entrysource) + (dst_positive_scale_hit_entrysource)) * S ((dst_positive_code_hit_entrysource) + (dst_positive_scale_hit_entrysource)) + ((dst_positive_scale_hit_entrysource) + (dst_positive_scale_hit_entrysource))) + (((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) * S ((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) + ((dst_negative_scale_hit_entrysource) + (dst_negative_scale_hit_entrysource)))) + ((((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) * S ((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) + ((dst_negative_scale_hit_entrysource) + (dst_negative_scale_hit_entrysource))) + (((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) * S ((dst_negative_code_hit_entrysource) + (dst_negative_scale_hit_entrysource)) + ((dst_negative_scale_hit_entrysource) + (dst_negative_scale_hit_entrysource)))))) /\ (((((exists ff_h_pvs_hit_entrysourcepositive. ff_h_pvs_hit_entrysourcepositive + S (dst_positive_hit_entrysource) = S ((S (i)) * dst_positive_scale_hit_entrysource)) /\ exists ff_q_pvs_hit_entrysourcepositive. dst_positive_code_hit_entrysource = ff_q_pvs_hit_entrysourcepositive * S ((S (i)) * dst_positive_scale_hit_entrysource) + (dst_positive_hit_entrysource))) /\ (((((exists ff_h_pvs_hit_entrysourcenegative. ff_h_pvs_hit_entrysourcenegative + S (dst_negative_hit_entrysource) = S ((S (i)) * dst_negative_scale_hit_entrysource)) /\ exists ff_q_pvs_hit_entrysourcenegative. dst_negative_code_hit_entrysource = ff_q_pvs_hit_entrysourcenegative * S ((S (i)) * dst_negative_scale_hit_entrysource) + (dst_negative_hit_entrysource))) /\ (exists ge_balance_positive_hit_entrysourcevalue ge_balance_negative_hit_entrysourcevalue. (((((ssr_entry_value_hit_entry) = 2 * (ge_balance_positive_hit_entrysourcevalue) /\ (ge_balance_negative_hit_entrysourcevalue) = 0) \/ exists ge_signed_half_hit_entrysourcevaluedecode. (((ssr_entry_value_hit_entry) = 2 * ge_signed_half_hit_entrysourcevaluedecode + 1 /\ (ge_balance_positive_hit_entrysourcevalue) = 0) /\ (ge_balance_negative_hit_entrysourcevalue) = S ge_signed_half_hit_entrysourcevaluedecode))) /\ ((dst_positive_hit_entrysource) + ge_balance_negative_hit_entrysourcevalue = (dst_negative_hit_entrysource) + ge_balance_positive_hit_entrysourcevalue))))))))) /\ (((((exists ff_h_pvs_hit_entrymap. ff_h_pvs_hit_entrymap + S (ssr_entry_image_hit_entry) = S ((S (i)) * s)) /\ exists ff_q_pvs_hit_entrymap. r = ff_q_pvs_hit_entrymap * S ((S (i)) * s) + (ssr_entry_image_hit_entry))) /\ (((((j)=(ssr_entry_image_hit_entry)) /\ ((a)=(ssr_entry_value_hit_entry)))) \/ (((~((j)=(ssr_entry_image_hit_entry))) /\ ((a)=0))))))))Constructive proof overview
Generated structural guide
An actual source lookup and actual beta image supply the retained incidence cell.
The unchanged tactic script uses 0 declared prerequisites and contains 18 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
none
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.
01Fix variables and assumptionsL1–8
02Construct an explicit witnessL9–10
03Separate the logical casesL11–11
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L11
split
04Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
exact ha
05Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
split
06Use earlier factsL14–14
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L14
exact hm