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 F. ((exists dst_positive_code_unit_witness_sourcepositive dst_positive_scale_unit_witness_sourcepositive dst_negative_code_unit_witness_sourcepositive dst_negative_scale_unit_witness_sourcepositive dst_positive_unit_witness_sourcepositive dst_negative_unit_witness_sourcepositive. (((F) = (((((dst_positive_code_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive)) * S ((dst_positive_code_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive)) + ((dst_positive_scale_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive))) + (((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) * S ((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) + ((dst_negative_scale_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)))) * S ((((dst_positive_code_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive)) * S ((dst_positive_code_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive)) + ((dst_positive_scale_unit_witness_sourcepositive) + (dst_positive_scale_unit_witness_sourcepositive))) + (((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) * S ((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) + ((dst_negative_scale_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)))) + ((((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) * S ((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) + ((dst_negative_scale_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive))) + (((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) * S ((dst_negative_code_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)) + ((dst_negative_scale_unit_witness_sourcepositive) + (dst_negative_scale_unit_witness_sourcepositive)))))) /\ (((((exists ff_h_pvs_unit_witness_sourcepositivepositive. ff_h_pvs_unit_witness_sourcepositivepositive + S (dst_positive_unit_witness_sourcepositive) = S ((S (1)) * dst_positive_scale_unit_witness_sourcepositive)) /\ exists ff_q_pvs_unit_witness_sourcepositivepositive. dst_positive_code_unit_witness_sourcepositive = ff_q_pvs_unit_witness_sourcepositivepositive * S ((S (1)) * dst_positive_scale_unit_witness_sourcepositive) + (dst_positive_unit_witness_sourcepositive))) /\ (((((exists ff_h_pvs_unit_witness_sourcepositivenegative. ff_h_pvs_unit_witness_sourcepositivenegative + S (dst_negative_unit_witness_sourcepositive) = S ((S (1)) * dst_negative_scale_unit_witness_sourcepositive)) /\ exists ff_q_pvs_unit_witness_sourcepositivenegative. dst_negative_code_unit_witness_sourcepositive = ff_q_pvs_unit_witness_sourcepositivenegative * S ((S (1)) * dst_negative_scale_unit_witness_sourcepositive) + (dst_negative_unit_witness_sourcepositive))) /\ (exists ge_balance_positive_unit_witness_sourcepositivevalue ge_balance_negative_unit_witness_sourcepositivevalue. (((((2) = 2 * (ge_balance_positive_unit_witness_sourcepositivevalue) /\ (ge_balance_negative_unit_witness_sourcepositivevalue) = 0) \/ exists ge_signed_half_unit_witness_sourcepositivevaluedecode. (((2) = 2 * ge_signed_half_unit_witness_sourcepositivevaluedecode + 1 /\ (ge_balance_positive_unit_witness_sourcepositivevalue) = 0) /\ (ge_balance_negative_unit_witness_sourcepositivevalue) = S ge_signed_half_unit_witness_sourcepositivevaluedecode))) /\ ((dst_positive_unit_witness_sourcepositive) + ge_balance_negative_unit_witness_sourcepositivevalue = (dst_negative_unit_witness_sourcepositive) + ge_balance_positive_unit_witness_sourcepositivevalue))))))))) \/ (exists dst_positive_code_unit_witness_sourcenegative dst_positive_scale_unit_witness_sourcenegative dst_negative_code_unit_witness_sourcenegative dst_negative_scale_unit_witness_sourcenegative dst_positive_unit_witness_sourcenegative dst_negative_unit_witness_sourcenegative. (((F) = (((((dst_positive_code_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative)) * S ((dst_positive_code_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative)) + ((dst_positive_scale_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative))) + (((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) * S ((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) + ((dst_negative_scale_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)))) * S ((((dst_positive_code_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative)) * S ((dst_positive_code_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative)) + ((dst_positive_scale_unit_witness_sourcenegative) + (dst_positive_scale_unit_witness_sourcenegative))) + (((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) * S ((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) + ((dst_negative_scale_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)))) + ((((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) * S ((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) + ((dst_negative_scale_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative))) + (((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) * S ((dst_negative_code_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)) + ((dst_negative_scale_unit_witness_sourcenegative) + (dst_negative_scale_unit_witness_sourcenegative)))))) /\ (((((exists ff_h_pvs_unit_witness_sourcenegativepositive. ff_h_pvs_unit_witness_sourcenegativepositive + S (dst_positive_unit_witness_sourcenegative) = S ((S (1)) * dst_positive_scale_unit_witness_sourcenegative)) /\ exists ff_q_pvs_unit_witness_sourcenegativepositive. dst_positive_code_unit_witness_sourcenegative = ff_q_pvs_unit_witness_sourcenegativepositive * S ((S (1)) * dst_positive_scale_unit_witness_sourcenegative) + (dst_positive_unit_witness_sourcenegative))) /\ (((((exists ff_h_pvs_unit_witness_sourcenegativenegative. ff_h_pvs_unit_witness_sourcenegativenegative + S (dst_negative_unit_witness_sourcenegative) = S ((S (1)) * dst_negative_scale_unit_witness_sourcenegative)) /\ exists ff_q_pvs_unit_witness_sourcenegativenegative. dst_negative_code_unit_witness_sourcenegative = ff_q_pvs_unit_witness_sourcenegativenegative * S ((S (1)) * dst_negative_scale_unit_witness_sourcenegative) + (dst_negative_unit_witness_sourcenegative))) /\ (exists ge_balance_positive_unit_witness_sourcenegativevalue ge_balance_negative_unit_witness_sourcenegativevalue. (((((1) = 2 * (ge_balance_positive_unit_witness_sourcenegativevalue) /\ (ge_balance_negative_unit_witness_sourcenegativevalue) = 0) \/ exists ge_signed_half_unit_witness_sourcenegativevaluedecode. (((1) = 2 * ge_signed_half_unit_witness_sourcenegativevaluedecode + 1 /\ (ge_balance_positive_unit_witness_sourcenegativevalue) = 0) /\ (ge_balance_negative_unit_witness_sourcenegativevalue) = S ge_signed_half_unit_witness_sourcenegativevaluedecode))) /\ ((dst_positive_unit_witness_sourcenegative) + ge_balance_negative_unit_witness_sourcenegativevalue = (dst_negative_unit_witness_sourcenegative) + ge_balance_positive_unit_witness_sourcenegativevalue)))))))))) -> exists u. ((exists dst_positive_code_unit_witness_entry dst_positive_scale_unit_witness_entry dst_negative_code_unit_witness_entry dst_negative_scale_unit_witness_entry dst_positive_unit_witness_entry dst_negative_unit_witness_entry. (((F) = (((((dst_positive_code_unit_witness_entry) + (dst_positive_scale_unit_witness_entry)) * S ((dst_positive_code_unit_witness_entry) + (dst_positive_scale_unit_witness_entry)) + ((dst_positive_scale_unit_witness_entry) + (dst_positive_scale_unit_witness_entry))) + (((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) * S ((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) + ((dst_negative_scale_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)))) * S ((((dst_positive_code_unit_witness_entry) + (dst_positive_scale_unit_witness_entry)) * S ((dst_positive_code_unit_witness_entry) + (dst_positive_scale_unit_witness_entry)) + ((dst_positive_scale_unit_witness_entry) + (dst_positive_scale_unit_witness_entry))) + (((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) * S ((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) + ((dst_negative_scale_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)))) + ((((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) * S ((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) + ((dst_negative_scale_unit_witness_entry) + (dst_negative_scale_unit_witness_entry))) + (((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) * S ((dst_negative_code_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)) + ((dst_negative_scale_unit_witness_entry) + (dst_negative_scale_unit_witness_entry)))))) /\ (((((exists ff_h_pvs_unit_witness_entrypositive. ff_h_pvs_unit_witness_entrypositive + S (dst_positive_unit_witness_entry) = S ((S (1)) * dst_positive_scale_unit_witness_entry)) /\ exists ff_q_pvs_unit_witness_entrypositive. dst_positive_code_unit_witness_entry = ff_q_pvs_unit_witness_entrypositive * S ((S (1)) * dst_positive_scale_unit_witness_entry) + (dst_positive_unit_witness_entry))) /\ (((((exists ff_h_pvs_unit_witness_entrynegative. ff_h_pvs_unit_witness_entrynegative + S (dst_negative_unit_witness_entry) = S ((S (1)) * dst_negative_scale_unit_witness_entry)) /\ exists ff_q_pvs_unit_witness_entrynegative. dst_negative_code_unit_witness_entry = ff_q_pvs_unit_witness_entrynegative * S ((S (1)) * dst_negative_scale_unit_witness_entry) + (dst_negative_unit_witness_entry))) /\ (exists ge_balance_positive_unit_witness_entryvalue ge_balance_negative_unit_witness_entryvalue. (((((u) = 2 * (ge_balance_positive_unit_witness_entryvalue) /\ (ge_balance_negative_unit_witness_entryvalue) = 0) \/ exists ge_signed_half_unit_witness_entryvaluedecode. (((u) = 2 * ge_signed_half_unit_witness_entryvaluedecode + 1 /\ (ge_balance_positive_unit_witness_entryvalue) = 0) /\ (ge_balance_negative_unit_witness_entryvalue) = S ge_signed_half_unit_witness_entryvaluedecode))) /\ ((dst_positive_unit_witness_entry) + ge_balance_negative_unit_witness_entryvalue = (dst_negative_unit_witness_entry) + ge_balance_positive_unit_witness_entryvalue))))))))) /\ (((u) = 2 \/ (u) = 1)))Constructive proof overview
Generated structural guide
An actual unit-at-one lookup supplies its canonical signed unit code; no inverse property is hidden in the predicate.
The unchanged tactic script uses 0 declared prerequisites and contains 13 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · 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 assumptionsL1–2
02Separate the logical casesL3–3
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L3
cases hu
03Construct an explicit witnessL4–4
Supply the displayed value, then prove that it has the required property.
- L4
exists 2
04Separate the logical casesL5–5
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L5
split
05Use earlier factsL6–6
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L6
exact hu_left
06Separate the logical casesL7–7
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L7
left
07Calculate and transport equalitiesL8–8
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L8
refl
08Construct an explicit witnessL9–9
Supply the displayed value, then prove that it has the required property.
- L9
exists 1
09Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
split
10Use earlier factsL11–11
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L11
exact hu_right
11Separate the logical casesL12–12
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L12
right
12Calculate and transport equalitiesL13–13
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L13
refl