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 k a. (exists dst_positive_code_miss_source dst_positive_scale_miss_source dst_negative_code_miss_source dst_negative_scale_miss_source dst_positive_miss_source dst_negative_miss_source. (((A) = (((((dst_positive_code_miss_source) + (dst_positive_scale_miss_source)) * S ((dst_positive_code_miss_source) + (dst_positive_scale_miss_source)) + ((dst_positive_scale_miss_source) + (dst_positive_scale_miss_source))) + (((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) * S ((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) + ((dst_negative_scale_miss_source) + (dst_negative_scale_miss_source)))) * S ((((dst_positive_code_miss_source) + (dst_positive_scale_miss_source)) * S ((dst_positive_code_miss_source) + (dst_positive_scale_miss_source)) + ((dst_positive_scale_miss_source) + (dst_positive_scale_miss_source))) + (((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) * S ((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) + ((dst_negative_scale_miss_source) + (dst_negative_scale_miss_source)))) + ((((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) * S ((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) + ((dst_negative_scale_miss_source) + (dst_negative_scale_miss_source))) + (((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) * S ((dst_negative_code_miss_source) + (dst_negative_scale_miss_source)) + ((dst_negative_scale_miss_source) + (dst_negative_scale_miss_source)))))) /\ (((((exists ff_h_pvs_miss_sourcepositive. ff_h_pvs_miss_sourcepositive + S (dst_positive_miss_source) = S ((S (i)) * dst_positive_scale_miss_source)) /\ exists ff_q_pvs_miss_sourcepositive. dst_positive_code_miss_source = ff_q_pvs_miss_sourcepositive * S ((S (i)) * dst_positive_scale_miss_source) + (dst_positive_miss_source))) /\ (((((exists ff_h_pvs_miss_sourcenegative. ff_h_pvs_miss_sourcenegative + S (dst_negative_miss_source) = S ((S (i)) * dst_negative_scale_miss_source)) /\ exists ff_q_pvs_miss_sourcenegative. dst_negative_code_miss_source = ff_q_pvs_miss_sourcenegative * S ((S (i)) * dst_negative_scale_miss_source) + (dst_negative_miss_source))) /\ (exists ge_balance_positive_miss_sourcevalue ge_balance_negative_miss_sourcevalue. (((((a) = 2 * (ge_balance_positive_miss_sourcevalue) /\ (ge_balance_negative_miss_sourcevalue) = 0) \/ exists ge_signed_half_miss_sourcevaluedecode. (((a) = 2 * ge_signed_half_miss_sourcevaluedecode + 1 /\ (ge_balance_positive_miss_sourcevalue) = 0) /\ (ge_balance_negative_miss_sourcevalue) = S ge_signed_half_miss_sourcevaluedecode))) /\ ((dst_positive_miss_source) + ge_balance_negative_miss_sourcevalue = (dst_negative_miss_source) + ge_balance_positive_miss_sourcevalue))))))))) -> (((exists ff_h_pvs_miss_map. ff_h_pvs_miss_map + S (k) = S ((S (i)) * s)) /\ exists ff_q_pvs_miss_map. r = ff_q_pvs_miss_map * S ((S (i)) * s) + (k))) -> ~(j=k) -> (exists ssr_entry_value_miss_entry ssr_entry_image_miss_entry. ((exists dst_positive_code_miss_entrysource dst_positive_scale_miss_entrysource dst_negative_code_miss_entrysource dst_negative_scale_miss_entrysource dst_positive_miss_entrysource dst_negative_miss_entrysource. (((A) = (((((dst_positive_code_miss_entrysource) + (dst_positive_scale_miss_entrysource)) * S ((dst_positive_code_miss_entrysource) + (dst_positive_scale_miss_entrysource)) + ((dst_positive_scale_miss_entrysource) + (dst_positive_scale_miss_entrysource))) + (((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) * S ((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) + ((dst_negative_scale_miss_entrysource) + (dst_negative_scale_miss_entrysource)))) * S ((((dst_positive_code_miss_entrysource) + (dst_positive_scale_miss_entrysource)) * S ((dst_positive_code_miss_entrysource) + (dst_positive_scale_miss_entrysource)) + ((dst_positive_scale_miss_entrysource) + (dst_positive_scale_miss_entrysource))) + (((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) * S ((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) + ((dst_negative_scale_miss_entrysource) + (dst_negative_scale_miss_entrysource)))) + ((((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) * S ((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) + ((dst_negative_scale_miss_entrysource) + (dst_negative_scale_miss_entrysource))) + (((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) * S ((dst_negative_code_miss_entrysource) + (dst_negative_scale_miss_entrysource)) + ((dst_negative_scale_miss_entrysource) + (dst_negative_scale_miss_entrysource)))))) /\ (((((exists ff_h_pvs_miss_entrysourcepositive. ff_h_pvs_miss_entrysourcepositive + S (dst_positive_miss_entrysource) = S ((S (i)) * dst_positive_scale_miss_entrysource)) /\ exists ff_q_pvs_miss_entrysourcepositive. dst_positive_code_miss_entrysource = ff_q_pvs_miss_entrysourcepositive * S ((S (i)) * dst_positive_scale_miss_entrysource) + (dst_positive_miss_entrysource))) /\ (((((exists ff_h_pvs_miss_entrysourcenegative. ff_h_pvs_miss_entrysourcenegative + S (dst_negative_miss_entrysource) = S ((S (i)) * dst_negative_scale_miss_entrysource)) /\ exists ff_q_pvs_miss_entrysourcenegative. dst_negative_code_miss_entrysource = ff_q_pvs_miss_entrysourcenegative * S ((S (i)) * dst_negative_scale_miss_entrysource) + (dst_negative_miss_entrysource))) /\ (exists ge_balance_positive_miss_entrysourcevalue ge_balance_negative_miss_entrysourcevalue. (((((ssr_entry_value_miss_entry) = 2 * (ge_balance_positive_miss_entrysourcevalue) /\ (ge_balance_negative_miss_entrysourcevalue) = 0) \/ exists ge_signed_half_miss_entrysourcevaluedecode. (((ssr_entry_value_miss_entry) = 2 * ge_signed_half_miss_entrysourcevaluedecode + 1 /\ (ge_balance_positive_miss_entrysourcevalue) = 0) /\ (ge_balance_negative_miss_entrysourcevalue) = S ge_signed_half_miss_entrysourcevaluedecode))) /\ ((dst_positive_miss_entrysource) + ge_balance_negative_miss_entrysourcevalue = (dst_negative_miss_entrysource) + ge_balance_positive_miss_entrysourcevalue))))))))) /\ (((((exists ff_h_pvs_miss_entrymap. ff_h_pvs_miss_entrymap + S (ssr_entry_image_miss_entry) = S ((S (i)) * s)) /\ exists ff_q_pvs_miss_entrymap. r = ff_q_pvs_miss_entrymap * S ((S (i)) * s) + (ssr_entry_image_miss_entry))) /\ (((((j)=(ssr_entry_image_miss_entry)) /\ ((0)=(ssr_entry_value_miss_entry)))) \/ (((~((j)=(ssr_entry_image_miss_entry))) /\ ((0)=0))))))))Constructive proof overview
Generated structural guide
An actual source lookup and beta image construct a zero cell at every different target index.
The unchanged tactic script uses 0 declared prerequisites and contains 20 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 assumptionsL1–10
02Construct an explicit witnessL11–12
03Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
split
04Use earlier factsL14–14
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L14
exact ha
05Separate the logical casesL15–15
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L15
split
06Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
exact hm
07Separate the logical casesL17–18
08Use earlier factsL19–19
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
exact hne
09Calculate and transport equalitiesL20–20
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L20
refl