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 p b c L t d e M. ((((L)=(t)+(M)) /\ (((forall fom_index_pfp_trim_length_sourceinput. (exists fom_gap_pfp_trim_length_sourceinput_index_bound. fom_gap_pfp_trim_length_sourceinput_index_bound + S (fom_index_pfp_trim_length_sourceinput) = L) -> exists fom_value_pfp_trim_length_sourceinput. ((((exists fom_beta_height_pfp_trim_length_sourceinput_entry. fom_beta_height_pfp_trim_length_sourceinput_entry + S (fom_value_pfp_trim_length_sourceinput) = S ((S (fom_index_pfp_trim_length_sourceinput)) * c)) /\ exists fom_beta_quotient_pfp_trim_length_sourceinput_entry. b = fom_beta_quotient_pfp_trim_length_sourceinput_entry * S ((S (fom_index_pfp_trim_length_sourceinput)) * c) + (fom_value_pfp_trim_length_sourceinput))) /\ (exists fom_gap_pfp_trim_length_sourceinput_value_bound. fom_gap_pfp_trim_length_sourceinput_value_bound + S (fom_value_pfp_trim_length_sourceinput) = p))) /\ (((forall pfp_repeat_index_trim_length_sourceremoved. (exists pfa_gap_trim_length_sourceremovedindex. pfa_gap_trim_length_sourceremovedindex + S (pfp_repeat_index_trim_length_sourceremoved) = (t)) -> (((exists ff_h_pfp_trim_length_sourceremovedentry. ff_h_pfp_trim_length_sourceremovedentry + S (0) = S ((S (pfp_repeat_index_trim_length_sourceremoved)) * c)) /\ exists ff_q_pfp_trim_length_sourceremovedentry. b = ff_q_pfp_trim_length_sourceremovedentry * S ((S (pfp_repeat_index_trim_length_sourceremoved)) * c) + (0)))) /\ (((forall pftrim_index_trim_length_sourcesuffix pftrim_value_trim_length_sourcesuffix. (exists pfa_gap_trim_length_sourcesuffixbound. pfa_gap_trim_length_sourcesuffixbound + S (pftrim_index_trim_length_sourcesuffix) = (M)) -> (((exists ff_h_pfp_trim_length_sourcesuffixsource. ff_h_pfp_trim_length_sourcesuffixsource + S (pftrim_value_trim_length_sourcesuffix) = S ((S ((t)+pftrim_index_trim_length_sourcesuffix)) * c)) /\ exists ff_q_pfp_trim_length_sourcesuffixsource. b = ff_q_pfp_trim_length_sourcesuffixsource * S ((S ((t)+pftrim_index_trim_length_sourcesuffix)) * c) + (pftrim_value_trim_length_sourcesuffix))) -> (((exists ff_h_pfp_trim_length_sourcesuffixoutput. ff_h_pfp_trim_length_sourcesuffixoutput + S (pftrim_value_trim_length_sourcesuffix) = S ((S (pftrim_index_trim_length_sourcesuffix)) * e)) /\ exists ff_q_pfp_trim_length_sourcesuffixoutput. d = ff_q_pfp_trim_length_sourcesuffixoutput * S ((S (pftrim_index_trim_length_sourcesuffix)) * e) + (pftrim_value_trim_length_sourcesuffix)))) /\ (((M)=0 \/ (exists pftrim_leading_trim_length_sourcenormal. ((((exists ff_h_pfp_trim_length_sourcenormalentry. ff_h_pfp_trim_length_sourcenormalentry + S (pftrim_leading_trim_length_sourcenormal) = S ((S (0)) * e)) /\ exists ff_q_pfp_trim_length_sourcenormalentry. d = ff_q_pfp_trim_length_sourcenormalentry * S ((S (0)) * e) + (pftrim_leading_trim_length_sourcenormal))) /\ ((~(pftrim_leading_trim_length_sourcenormal=0))))))))))))))) -> ((exists pftrim_gap_removed_bound. pftrim_gap_removed_bound+(t)=(L)) /\ ((exists pftrim_gap_retained_bound. pftrim_gap_retained_bound+(M)=(L))))Constructive proof overview
Generated structural guide
Both the number of removed leading zeroes and the retained length are bounded by the actual annotated input length.
The unchanged tactic script uses 1 declared prerequisite and contains 22 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
add_comm Stable 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 assumptionsL1–9
02Separate the logical casesL10–14
03Construct an explicit witnessL15–15
Supply the displayed value, then prove that it has the required property.
- L15
exists M
04Calculate and transport equalitiesL16–16
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L16
trans t+M
05Use earlier factsL17–17
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L17
apply add_comm
06Calculate and transport equalitiesL18–18
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L18
symm
07Use earlier factsL19–19
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
exact h_left
08Construct an explicit witnessL20–20
Supply the displayed value, then prove that it has the required property.
- L20
exists t
09Calculate and transport equalitiesL21–21
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L21
symm
10Use earlier factsL22–22
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L22
exact h_left