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 b c L d e. (((forall mdr_i_pfp_shift_power_zero_relationprefix mdr_a_pfp_shift_power_zero_relationprefix. (exists mdr_gap_pfp_shift_power_zero_relationprefixb. mdr_gap_pfp_shift_power_zero_relationprefixb + S (mdr_i_pfp_shift_power_zero_relationprefix) = (L)) -> (((exists ff_h_mdr_pfp_shift_power_zero_relationprefixo. ff_h_mdr_pfp_shift_power_zero_relationprefixo + S (mdr_a_pfp_shift_power_zero_relationprefix) = S ((S (mdr_i_pfp_shift_power_zero_relationprefix)) * c)) /\ exists ff_q_mdr_pfp_shift_power_zero_relationprefixo. b = ff_q_mdr_pfp_shift_power_zero_relationprefixo * S ((S (mdr_i_pfp_shift_power_zero_relationprefix)) * c) + (mdr_a_pfp_shift_power_zero_relationprefix))) -> (((exists ff_h_mdr_pfp_shift_power_zero_relationprefixn. ff_h_mdr_pfp_shift_power_zero_relationprefixn + S (mdr_a_pfp_shift_power_zero_relationprefix) = S ((S (mdr_i_pfp_shift_power_zero_relationprefix)) * e)) /\ exists ff_q_mdr_pfp_shift_power_zero_relationprefixn. d = ff_q_mdr_pfp_shift_power_zero_relationprefixn * S ((S (mdr_i_pfp_shift_power_zero_relationprefix)) * e) + (mdr_a_pfp_shift_power_zero_relationprefix)))) /\ ((((exists ff_h_pfp_shift_power_zero_relationlast. ff_h_pfp_shift_power_zero_relationlast + S (0) = S ((S (L)) * e)) /\ exists ff_q_pfp_shift_power_zero_relationlast. d = ff_q_pfp_shift_power_zero_relationlast * S ((S (L)) * e) + (0)))))) -> ((exists pfrep_position_shift_power_zero_result. ((pfrep_position_shift_power_zero_result+S (0)=(S L)) /\ ((((exists ff_h_pfp_shift_power_zero_resultentry. ff_h_pfp_shift_power_zero_resultentry + S (0) = S ((S (pfrep_position_shift_power_zero_result)) * e)) /\ exists ff_q_pfp_shift_power_zero_resultentry. d = ff_q_pfp_shift_power_zero_resultentry * S ((S (pfrep_position_shift_power_zero_result)) * e) + (0)))))) \/ (((exists pfrep_gap_shift_power_zero_resultoutside. pfrep_gap_shift_power_zero_resultoutside+(S L)=(0)) /\ (((0)=0)))))Constructive proof overview
Generated structural guide
The actual constant coefficient of a trailing-zero shift is zero, even when the original representation is empty.
The unchanged tactic script uses 0 declared prerequisites and contains 12 exact native proof lines.
Alpha v34 checked-use · first admitted v34 · 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.
01Fix variables and assumptionsL1–6
02Separate the logical casesL7–8
03Construct an explicit witnessL9–9
Supply the displayed value, then prove that it has the required property.
- L9
exists L
04Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
split
05Calculate and transport equalitiesL11–11
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L11
simp
06Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
exact hs_right