MX0043

signed_support_incidence_exists

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Construct an actual padded incidence table for every pair of finite dimensions, including either zero dimension.

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 L M. (exists dst_positive_code_grid_source_table dst_positive_scale_grid_source_table dst_negative_code_grid_source_table dst_negative_scale_grid_source_table. (((A) = (((((dst_positive_code_grid_source_table) + (dst_positive_scale_grid_source_table)) * S ((dst_positive_code_grid_source_table) + (dst_positive_scale_grid_source_table)) + ((dst_positive_scale_grid_source_table) + (dst_positive_scale_grid_source_table))) + (((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) * S ((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) + ((dst_negative_scale_grid_source_table) + (dst_negative_scale_grid_source_table)))) * S ((((dst_positive_code_grid_source_table) + (dst_positive_scale_grid_source_table)) * S ((dst_positive_code_grid_source_table) + (dst_positive_scale_grid_source_table)) + ((dst_positive_scale_grid_source_table) + (dst_positive_scale_grid_source_table))) + (((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) * S ((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) + ((dst_negative_scale_grid_source_table) + (dst_negative_scale_grid_source_table)))) + ((((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) * S ((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) + ((dst_negative_scale_grid_source_table) + (dst_negative_scale_grid_source_table))) + (((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) * S ((dst_negative_code_grid_source_table) + (dst_negative_scale_grid_source_table)) + ((dst_negative_scale_grid_source_table) + (dst_negative_scale_grid_source_table)))))) /\ (forall dst_index_grid_source_table. (exists pvs_le_gap_grid_source_tabledomain. pvs_le_gap_grid_source_tabledomain + (dst_index_grid_source_table) = (0)) -> exists dst_positive_grid_source_table dst_negative_grid_source_table dst_value_grid_source_table. ((((exists ff_h_pvs_grid_source_tableentrypositive. ff_h_pvs_grid_source_tableentrypositive + S (dst_positive_grid_source_table) = S ((S (dst_index_grid_source_table)) * dst_positive_scale_grid_source_table)) /\ exists ff_q_pvs_grid_source_tableentrypositive. dst_positive_code_grid_source_table = ff_q_pvs_grid_source_tableentrypositive * S ((S (dst_index_grid_source_table)) * dst_positive_scale_grid_source_table) + (dst_positive_grid_source_table))) /\ (((((exists ff_h_pvs_grid_source_tableentrynegative. ff_h_pvs_grid_source_tableentrynegative + S (dst_negative_grid_source_table) = S ((S (dst_index_grid_source_table)) * dst_negative_scale_grid_source_table)) /\ exists ff_q_pvs_grid_source_tableentrynegative. dst_negative_code_grid_source_table = ff_q_pvs_grid_source_tableentrynegative * S ((S (dst_index_grid_source_table)) * dst_negative_scale_grid_source_table) + (dst_negative_grid_source_table))) /\ (exists ge_balance_positive_grid_source_tableentryvalue ge_balance_negative_grid_source_tableentryvalue. (((((dst_value_grid_source_table) = 2 * (ge_balance_positive_grid_source_tableentryvalue) /\ (ge_balance_negative_grid_source_tableentryvalue) = 0) \/ exists ge_signed_half_grid_source_tableentryvaluedecode. (((dst_value_grid_source_table) = 2 * ge_signed_half_grid_source_tableentryvaluedecode + 1 /\ (ge_balance_positive_grid_source_tableentryvalue) = 0) /\ (ge_balance_negative_grid_source_tableentryvalue) = S ge_signed_half_grid_source_tableentryvaluedecode))) /\ ((dst_positive_grid_source_table) + ge_balance_negative_grid_source_tableentryvalue = (dst_negative_grid_source_table) + ge_balance_positive_grid_source_tableentryvalue))))))))) -> exists T. (((exists dst_positive_code_grid_existssource dst_positive_scale_grid_existssource dst_negative_code_grid_existssource dst_negative_scale_grid_existssource. (((A) = (((((dst_positive_code_grid_existssource) + (dst_positive_scale_grid_existssource)) * S ((dst_positive_code_grid_existssource) + (dst_positive_scale_grid_existssource)) + ((dst_positive_scale_grid_existssource) + (dst_positive_scale_grid_existssource))) + (((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) * S ((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) + ((dst_negative_scale_grid_existssource) + (dst_negative_scale_grid_existssource)))) * S ((((dst_positive_code_grid_existssource) + (dst_positive_scale_grid_existssource)) * S ((dst_positive_code_grid_existssource) + (dst_positive_scale_grid_existssource)) + ((dst_positive_scale_grid_existssource) + (dst_positive_scale_grid_existssource))) + (((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) * S ((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) + ((dst_negative_scale_grid_existssource) + (dst_negative_scale_grid_existssource)))) + ((((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) * S ((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) + ((dst_negative_scale_grid_existssource) + (dst_negative_scale_grid_existssource))) + (((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) * S ((dst_negative_code_grid_existssource) + (dst_negative_scale_grid_existssource)) + ((dst_negative_scale_grid_existssource) + (dst_negative_scale_grid_existssource)))))) /\ (forall dst_index_grid_existssource. (exists pvs_le_gap_grid_existssourcedomain. pvs_le_gap_grid_existssourcedomain + (dst_index_grid_existssource) = (0)) -> exists dst_positive_grid_existssource dst_negative_grid_existssource dst_value_grid_existssource. ((((exists ff_h_pvs_grid_existssourceentrypositive. ff_h_pvs_grid_existssourceentrypositive + S (dst_positive_grid_existssource) = S ((S (dst_index_grid_existssource)) * dst_positive_scale_grid_existssource)) /\ exists ff_q_pvs_grid_existssourceentrypositive. dst_positive_code_grid_existssource = ff_q_pvs_grid_existssourceentrypositive * S ((S (dst_index_grid_existssource)) * dst_positive_scale_grid_existssource) + (dst_positive_grid_existssource))) /\ (((((exists ff_h_pvs_grid_existssourceentrynegative. ff_h_pvs_grid_existssourceentrynegative + S (dst_negative_grid_existssource) = S ((S (dst_index_grid_existssource)) * dst_negative_scale_grid_existssource)) /\ exists ff_q_pvs_grid_existssourceentrynegative. dst_negative_code_grid_existssource = ff_q_pvs_grid_existssourceentrynegative * S ((S (dst_index_grid_existssource)) * dst_negative_scale_grid_existssource) + (dst_negative_grid_existssource))) /\ (exists ge_balance_positive_grid_existssourceentryvalue ge_balance_negative_grid_existssourceentryvalue. (((((dst_value_grid_existssource) = 2 * (ge_balance_positive_grid_existssourceentryvalue) /\ (ge_balance_negative_grid_existssourceentryvalue) = 0) \/ exists ge_signed_half_grid_existssourceentryvaluedecode. (((dst_value_grid_existssource) = 2 * ge_signed_half_grid_existssourceentryvaluedecode + 1 /\ (ge_balance_positive_grid_existssourceentryvalue) = 0) /\ (ge_balance_negative_grid_existssourceentryvalue) = S ge_signed_half_grid_existssourceentryvaluedecode))) /\ ((dst_positive_grid_existssource) + ge_balance_negative_grid_existssourceentryvalue = (dst_negative_grid_existssource) + ge_balance_positive_grid_existssourceentryvalue))))))))) /\ (((exists dst_positive_code_grid_existstable dst_positive_scale_grid_existstable dst_negative_code_grid_existstable dst_negative_scale_grid_existstable. (((T) = (((((dst_positive_code_grid_existstable) + (dst_positive_scale_grid_existstable)) * S ((dst_positive_code_grid_existstable) + (dst_positive_scale_grid_existstable)) + ((dst_positive_scale_grid_existstable) + (dst_positive_scale_grid_existstable))) + (((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) * S ((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) + ((dst_negative_scale_grid_existstable) + (dst_negative_scale_grid_existstable)))) * S ((((dst_positive_code_grid_existstable) + (dst_positive_scale_grid_existstable)) * S ((dst_positive_code_grid_existstable) + (dst_positive_scale_grid_existstable)) + ((dst_positive_scale_grid_existstable) + (dst_positive_scale_grid_existstable))) + (((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) * S ((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) + ((dst_negative_scale_grid_existstable) + (dst_negative_scale_grid_existstable)))) + ((((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) * S ((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) + ((dst_negative_scale_grid_existstable) + (dst_negative_scale_grid_existstable))) + (((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) * S ((dst_negative_code_grid_existstable) + (dst_negative_scale_grid_existstable)) + ((dst_negative_scale_grid_existstable) + (dst_negative_scale_grid_existstable)))))) /\ (forall dst_index_grid_existstable. (exists pvs_le_gap_grid_existstabledomain. pvs_le_gap_grid_existstabledomain + (dst_index_grid_existstable) = ((L)*(S (M)))) -> exists dst_positive_grid_existstable dst_negative_grid_existstable dst_value_grid_existstable. ((((exists ff_h_pvs_grid_existstableentrypositive. ff_h_pvs_grid_existstableentrypositive + S (dst_positive_grid_existstable) = S ((S (dst_index_grid_existstable)) * dst_positive_scale_grid_existstable)) /\ exists ff_q_pvs_grid_existstableentrypositive. dst_positive_code_grid_existstable = ff_q_pvs_grid_existstableentrypositive * S ((S (dst_index_grid_existstable)) * dst_positive_scale_grid_existstable) + (dst_positive_grid_existstable))) /\ (((((exists ff_h_pvs_grid_existstableentrynegative. ff_h_pvs_grid_existstableentrynegative + S (dst_negative_grid_existstable) = S ((S (dst_index_grid_existstable)) * dst_negative_scale_grid_existstable)) /\ exists ff_q_pvs_grid_existstableentrynegative. dst_negative_code_grid_existstable = ff_q_pvs_grid_existstableentrynegative * S ((S (dst_index_grid_existstable)) * dst_negative_scale_grid_existstable) + (dst_negative_grid_existstable))) /\ (exists ge_balance_positive_grid_existstableentryvalue ge_balance_negative_grid_existstableentryvalue. (((((dst_value_grid_existstable) = 2 * (ge_balance_positive_grid_existstableentryvalue) /\ (ge_balance_negative_grid_existstableentryvalue) = 0) \/ exists ge_signed_half_grid_existstableentryvaluedecode. (((dst_value_grid_existstable) = 2 * ge_signed_half_grid_existstableentryvaluedecode + 1 /\ (ge_balance_positive_grid_existstableentryvalue) = 0) /\ (ge_balance_negative_grid_existstableentryvalue) = S ge_signed_half_grid_existstableentryvaluedecode))) /\ ((dst_positive_grid_existstable) + ge_balance_negative_grid_existstableentryvalue = (dst_negative_grid_existstable) + ge_balance_positive_grid_existstableentryvalue))))))))) /\ (forall ssr_grid_row_grid_exists ssr_grid_column_grid_exists ssr_grid_value_grid_exists. (exists pvs_gap_grid_existsrow_bound. pvs_gap_grid_existsrow_bound + S (ssr_grid_row_grid_exists) = (L)) -> (exists pvs_gap_grid_existscolumn_bound. pvs_gap_grid_existscolumn_bound + S (ssr_grid_column_grid_exists) = (M)) -> (exists dst_positive_code_grid_existslookup dst_positive_scale_grid_existslookup dst_negative_code_grid_existslookup dst_negative_scale_grid_existslookup dst_positive_grid_existslookup dst_negative_grid_existslookup. (((T) = (((((dst_positive_code_grid_existslookup) + (dst_positive_scale_grid_existslookup)) * S ((dst_positive_code_grid_existslookup) + (dst_positive_scale_grid_existslookup)) + ((dst_positive_scale_grid_existslookup) + (dst_positive_scale_grid_existslookup))) + (((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) * S ((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) + ((dst_negative_scale_grid_existslookup) + (dst_negative_scale_grid_existslookup)))) * S ((((dst_positive_code_grid_existslookup) + (dst_positive_scale_grid_existslookup)) * S ((dst_positive_code_grid_existslookup) + (dst_positive_scale_grid_existslookup)) + ((dst_positive_scale_grid_existslookup) + (dst_positive_scale_grid_existslookup))) + (((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) * S ((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) + ((dst_negative_scale_grid_existslookup) + (dst_negative_scale_grid_existslookup)))) + ((((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) * S ((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) + ((dst_negative_scale_grid_existslookup) + (dst_negative_scale_grid_existslookup))) + (((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) * S ((dst_negative_code_grid_existslookup) + (dst_negative_scale_grid_existslookup)) + ((dst_negative_scale_grid_existslookup) + (dst_negative_scale_grid_existslookup)))))) /\ (((((exists ff_h_pvs_grid_existslookuppositive. ff_h_pvs_grid_existslookuppositive + S (dst_positive_grid_existslookup) = S ((S (((S (M))*(ssr_grid_row_grid_exists)+(ssr_grid_column_grid_exists)))) * dst_positive_scale_grid_existslookup)) /\ exists ff_q_pvs_grid_existslookuppositive. dst_positive_code_grid_existslookup = ff_q_pvs_grid_existslookuppositive * S ((S (((S (M))*(ssr_grid_row_grid_exists)+(ssr_grid_column_grid_exists)))) * dst_positive_scale_grid_existslookup) + (dst_positive_grid_existslookup))) /\ (((((exists ff_h_pvs_grid_existslookupnegative. ff_h_pvs_grid_existslookupnegative + S (dst_negative_grid_existslookup) = S ((S (((S (M))*(ssr_grid_row_grid_exists)+(ssr_grid_column_grid_exists)))) * dst_negative_scale_grid_existslookup)) /\ exists ff_q_pvs_grid_existslookupnegative. dst_negative_code_grid_existslookup = ff_q_pvs_grid_existslookupnegative * S ((S (((S (M))*(ssr_grid_row_grid_exists)+(ssr_grid_column_grid_exists)))) * dst_negative_scale_grid_existslookup) + (dst_negative_grid_existslookup))) /\ (exists ge_balance_positive_grid_existslookupvalue ge_balance_negative_grid_existslookupvalue. (((((ssr_grid_value_grid_exists) = 2 * (ge_balance_positive_grid_existslookupvalue) /\ (ge_balance_negative_grid_existslookupvalue) = 0) \/ exists ge_signed_half_grid_existslookupvaluedecode. (((ssr_grid_value_grid_exists) = 2 * ge_signed_half_grid_existslookupvaluedecode + 1 /\ (ge_balance_positive_grid_existslookupvalue) = 0) /\ (ge_balance_negative_grid_existslookupvalue) = S ge_signed_half_grid_existslookupvaluedecode))) /\ ((dst_positive_grid_existslookup) + ge_balance_negative_grid_existslookupvalue = (dst_negative_grid_existslookup) + ge_balance_positive_grid_existslookupvalue))))))))) -> (exists ssr_entry_value_grid_existsentry ssr_entry_image_grid_existsentry. ((exists dst_positive_code_grid_existsentrysource dst_positive_scale_grid_existsentrysource dst_negative_code_grid_existsentrysource dst_negative_scale_grid_existsentrysource dst_positive_grid_existsentrysource dst_negative_grid_existsentrysource. (((A) = (((((dst_positive_code_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource)) * S ((dst_positive_code_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource)) + ((dst_positive_scale_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource))) + (((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) * S ((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) + ((dst_negative_scale_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)))) * S ((((dst_positive_code_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource)) * S ((dst_positive_code_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource)) + ((dst_positive_scale_grid_existsentrysource) + (dst_positive_scale_grid_existsentrysource))) + (((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) * S ((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) + ((dst_negative_scale_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)))) + ((((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) * S ((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) + ((dst_negative_scale_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource))) + (((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) * S ((dst_negative_code_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)) + ((dst_negative_scale_grid_existsentrysource) + (dst_negative_scale_grid_existsentrysource)))))) /\ (((((exists ff_h_pvs_grid_existsentrysourcepositive. ff_h_pvs_grid_existsentrysourcepositive + S (dst_positive_grid_existsentrysource) = S ((S (ssr_grid_row_grid_exists)) * dst_positive_scale_grid_existsentrysource)) /\ exists ff_q_pvs_grid_existsentrysourcepositive. dst_positive_code_grid_existsentrysource = ff_q_pvs_grid_existsentrysourcepositive * S ((S (ssr_grid_row_grid_exists)) * dst_positive_scale_grid_existsentrysource) + (dst_positive_grid_existsentrysource))) /\ (((((exists ff_h_pvs_grid_existsentrysourcenegative. ff_h_pvs_grid_existsentrysourcenegative + S (dst_negative_grid_existsentrysource) = S ((S (ssr_grid_row_grid_exists)) * dst_negative_scale_grid_existsentrysource)) /\ exists ff_q_pvs_grid_existsentrysourcenegative. dst_negative_code_grid_existsentrysource = ff_q_pvs_grid_existsentrysourcenegative * S ((S (ssr_grid_row_grid_exists)) * dst_negative_scale_grid_existsentrysource) + (dst_negative_grid_existsentrysource))) /\ (exists ge_balance_positive_grid_existsentrysourcevalue ge_balance_negative_grid_existsentrysourcevalue. (((((ssr_entry_value_grid_existsentry) = 2 * (ge_balance_positive_grid_existsentrysourcevalue) /\ (ge_balance_negative_grid_existsentrysourcevalue) = 0) \/ exists ge_signed_half_grid_existsentrysourcevaluedecode. (((ssr_entry_value_grid_existsentry) = 2 * ge_signed_half_grid_existsentrysourcevaluedecode + 1 /\ (ge_balance_positive_grid_existsentrysourcevalue) = 0) /\ (ge_balance_negative_grid_existsentrysourcevalue) = S ge_signed_half_grid_existsentrysourcevaluedecode))) /\ ((dst_positive_grid_existsentrysource) + ge_balance_negative_grid_existsentrysourcevalue = (dst_negative_grid_existsentrysource) + ge_balance_positive_grid_existsentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_grid_existsentrymap. ff_h_pvs_grid_existsentrymap + S (ssr_entry_image_grid_existsentry) = S ((S (ssr_grid_row_grid_exists)) * s)) /\ exists ff_q_pvs_grid_existsentrymap. r = ff_q_pvs_grid_existsentrymap * S ((S (ssr_grid_row_grid_exists)) * s) + (ssr_entry_image_grid_existsentry))) /\ (((((ssr_grid_column_grid_exists)=(ssr_entry_image_grid_existsentry)) /\ ((ssr_grid_value_grid_exists)=(ssr_entry_value_grid_existsentry)))) \/ (((~((ssr_grid_column_grid_exists)=(ssr_entry_image_grid_existsentry))) /\ ((ssr_grid_value_grid_exists)=0)))))))))))))

Constructive proof overview

Generated structural guide

Construct an actual padded incidence table for every pair of finite dimensions, including either zero dimension.

The unchanged tactic script uses 2 declared prerequisites and contains 25 exact native proof lines.

Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

MX0041 signed_support_incidence_flat_prefix_exists MX0042 signed_support_incidence_from_flat_prefix

Direct dependents

MX004A signed_support_reindex_sum_equal

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

25 script commands · 5 reading checkpoints · 1 local claims

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.

Named ingredients (2)
signed support incidence flat prefix existssigned support incidence from flat prefix

Long local formulas use this family’s existing definitions. Each new abbreviation was expanded back to the identical native formula, including its free-variable context. The original edition is preserved below.

01Fix variables and assumptionsL1–6

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro A
  2. L2
    intro r
  3. L3
    intro s
  4. L4
    intro L
  5. L5
    intro M
  6. L6
    intro hA
02Establish hpL7–14

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed support incidence flat prefix exists.

  1. L7
    have hp : ∃ T. SignedIncidenceFlatPrefix(A,r,s,M,L · S M,T)Definitions: SignedIncidenceFlatPrefix
  2. L8
    specialize signed_support_incidence_flat_prefix_exists (A)
  3. L9
    specialize signed_support_incidence_flat_prefix_exists (r)
  4. L10
    specialize signed_support_incidence_flat_prefix_exists (s)
  5. L11
    specialize signed_support_incidence_flat_prefix_exists (M)
  6. L12
    specialize signed_support_incidence_flat_prefix_exists (L*(S M))
  7. L13
    apply signed_support_incidence_flat_prefix_exists
  8. L14
    exact hA
03Separate the logical casesL15–15

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L15
    cases hp
04Construct an explicit witnessL16–16

Supply the displayed value, then prove that it has the required property.

  1. L16
    exists x
05Use earlier factsL17–25

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L17
    specialize signed_support_incidence_from_flat_prefix (A)
  2. L18
    specialize signed_support_incidence_from_flat_prefix (r)
  3. L19
    specialize signed_support_incidence_from_flat_prefix (s)
  4. L20
    specialize signed_support_incidence_from_flat_prefix (L)
  5. L21
    specialize signed_support_incidence_from_flat_prefix (M)
  6. L22
    specialize signed_support_incidence_from_flat_prefix (x)
  7. L23
    apply signed_support_incidence_from_flat_prefix
  8. L24
    exact hA
  9. L25
    exact hp_witness

Library-wide reading audit

Original exact command ledger · 25 lines
  1. 0001intro A
  2. 0002intro r
  3. 0003intro s
  4. 0004intro L
  5. 0005intro M
  6. 0006intro hA
  7. 0007have hp : exists T. (((exists dst_positive_code_grid_flattable dst_positive_scale_grid_flattable dst_negative_code_grid_flattable dst_negative_scale_grid_flattable. (((T) = (((((dst_positive_code_grid_flattable) + (dst_positive_scale_grid_flattable)) * S ((dst_positive_code_grid_flattable) + (dst_positive_scale_grid_flattable)) + ((dst_positive_scale_grid_flattable) + (dst_positive_scale_grid_flattable))) + (((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) * S ((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) + ((dst_negative_scale_grid_flattable) + (dst_negative_scale_grid_flattable)))) * S ((((dst_positive_code_grid_flattable) + (dst_positive_scale_grid_flattable)) * S ((dst_positive_code_grid_flattable) + (dst_positive_scale_grid_flattable)) + ((dst_positive_scale_grid_flattable) + (dst_positive_scale_grid_flattable))) + (((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) * S ((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) + ((dst_negative_scale_grid_flattable) + (dst_negative_scale_grid_flattable)))) + ((((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) * S ((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) + ((dst_negative_scale_grid_flattable) + (dst_negative_scale_grid_flattable))) + (((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) * S ((dst_negative_code_grid_flattable) + (dst_negative_scale_grid_flattable)) + ((dst_negative_scale_grid_flattable) + (dst_negative_scale_grid_flattable)))))) /\ (forall dst_index_grid_flattable. (exists pvs_le_gap_grid_flattabledomain. pvs_le_gap_grid_flattabledomain + (dst_index_grid_flattable) = (L*(S M))) -> exists dst_positive_grid_flattable dst_negative_grid_flattable dst_value_grid_flattable. ((((exists ff_h_pvs_grid_flattableentrypositive. ff_h_pvs_grid_flattableentrypositive + S (dst_positive_grid_flattable) = S ((S (dst_index_grid_flattable)) * dst_positive_scale_grid_flattable)) /\ exists ff_q_pvs_grid_flattableentrypositive. dst_positive_code_grid_flattable = ff_q_pvs_grid_flattableentrypositive * S ((S (dst_index_grid_flattable)) * dst_positive_scale_grid_flattable) + (dst_positive_grid_flattable))) /\ (((((exists ff_h_pvs_grid_flattableentrynegative. ff_h_pvs_grid_flattableentrynegative + S (dst_negative_grid_flattable) = S ((S (dst_index_grid_flattable)) * dst_negative_scale_grid_flattable)) /\ exists ff_q_pvs_grid_flattableentrynegative. dst_negative_code_grid_flattable = ff_q_pvs_grid_flattableentrynegative * S ((S (dst_index_grid_flattable)) * dst_negative_scale_grid_flattable) + (dst_negative_grid_flattable))) /\ (exists ge_balance_positive_grid_flattableentryvalue ge_balance_negative_grid_flattableentryvalue. (((((dst_value_grid_flattable) = 2 * (ge_balance_positive_grid_flattableentryvalue) /\ (ge_balance_negative_grid_flattableentryvalue) = 0) \/ exists ge_signed_half_grid_flattableentryvaluedecode. (((dst_value_grid_flattable) = 2 * ge_signed_half_grid_flattableentryvaluedecode + 1 /\ (ge_balance_positive_grid_flattableentryvalue) = 0) /\ (ge_balance_negative_grid_flattableentryvalue) = S ge_signed_half_grid_flattableentryvaluedecode))) /\ ((dst_positive_grid_flattable) + ge_balance_negative_grid_flattableentryvalue = (dst_negative_grid_flattable) + ge_balance_positive_grid_flattableentryvalue))))))))) /\ (forall ssr_prefix_index_grid_flat ssr_prefix_value_grid_flat. (exists pvs_le_gap_grid_flatbound. pvs_le_gap_grid_flatbound + (ssr_prefix_index_grid_flat) = (L*(S M))) -> (exists dst_positive_code_grid_flatlookup dst_positive_scale_grid_flatlookup dst_negative_code_grid_flatlookup dst_negative_scale_grid_flatlookup dst_positive_grid_flatlookup dst_negative_grid_flatlookup. (((T) = (((((dst_positive_code_grid_flatlookup) + (dst_positive_scale_grid_flatlookup)) * S ((dst_positive_code_grid_flatlookup) + (dst_positive_scale_grid_flatlookup)) + ((dst_positive_scale_grid_flatlookup) + (dst_positive_scale_grid_flatlookup))) + (((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) * S ((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) + ((dst_negative_scale_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)))) * S ((((dst_positive_code_grid_flatlookup) + (dst_positive_scale_grid_flatlookup)) * S ((dst_positive_code_grid_flatlookup) + (dst_positive_scale_grid_flatlookup)) + ((dst_positive_scale_grid_flatlookup) + (dst_positive_scale_grid_flatlookup))) + (((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) * S ((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) + ((dst_negative_scale_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)))) + ((((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) * S ((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) + ((dst_negative_scale_grid_flatlookup) + (dst_negative_scale_grid_flatlookup))) + (((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) * S ((dst_negative_code_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)) + ((dst_negative_scale_grid_flatlookup) + (dst_negative_scale_grid_flatlookup)))))) /\ (((((exists ff_h_pvs_grid_flatlookuppositive. ff_h_pvs_grid_flatlookuppositive + S (dst_positive_grid_flatlookup) = S ((S (ssr_prefix_index_grid_flat)) * dst_positive_scale_grid_flatlookup)) /\ exists ff_q_pvs_grid_flatlookuppositive. dst_positive_code_grid_flatlookup = ff_q_pvs_grid_flatlookuppositive * S ((S (ssr_prefix_index_grid_flat)) * dst_positive_scale_grid_flatlookup) + (dst_positive_grid_flatlookup))) /\ (((((exists ff_h_pvs_grid_flatlookupnegative. ff_h_pvs_grid_flatlookupnegative + S (dst_negative_grid_flatlookup) = S ((S (ssr_prefix_index_grid_flat)) * dst_negative_scale_grid_flatlookup)) /\ exists ff_q_pvs_grid_flatlookupnegative. dst_negative_code_grid_flatlookup = ff_q_pvs_grid_flatlookupnegative * S ((S (ssr_prefix_index_grid_flat)) * dst_negative_scale_grid_flatlookup) + (dst_negative_grid_flatlookup))) /\ (exists ge_balance_positive_grid_flatlookupvalue ge_balance_negative_grid_flatlookupvalue. (((((ssr_prefix_value_grid_flat) = 2 * (ge_balance_positive_grid_flatlookupvalue) /\ (ge_balance_negative_grid_flatlookupvalue) = 0) \/ exists ge_signed_half_grid_flatlookupvaluedecode. (((ssr_prefix_value_grid_flat) = 2 * ge_signed_half_grid_flatlookupvaluedecode + 1 /\ (ge_balance_positive_grid_flatlookupvalue) = 0) /\ (ge_balance_negative_grid_flatlookupvalue) = S ge_signed_half_grid_flatlookupvaluedecode))) /\ ((dst_positive_grid_flatlookup) + ge_balance_negative_grid_flatlookupvalue = (dst_negative_grid_flatlookup) + ge_balance_positive_grid_flatlookupvalue))))))))) -> (exists ssr_flat_row_grid_flatentry ssr_flat_column_grid_flatentry. (((ssr_prefix_index_grid_flat)=(((S (M))*(ssr_flat_row_grid_flatentry)+(ssr_flat_column_grid_flatentry)))) /\ (((exists pvs_gap_grid_flatentryremainder. pvs_gap_grid_flatentryremainder + S (ssr_flat_column_grid_flatentry) = (S (M))) /\ (exists ssr_entry_value_grid_flatentryentry ssr_entry_image_grid_flatentryentry. ((exists dst_positive_code_grid_flatentryentrysource dst_positive_scale_grid_flatentryentrysource dst_negative_code_grid_flatentryentrysource dst_negative_scale_grid_flatentryentrysource dst_positive_grid_flatentryentrysource dst_negative_grid_flatentryentrysource. (((A) = (((((dst_positive_code_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource)) * S ((dst_positive_code_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource)) + ((dst_positive_scale_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource))) + (((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) * S ((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) + ((dst_negative_scale_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)))) * S ((((dst_positive_code_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource)) * S ((dst_positive_code_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource)) + ((dst_positive_scale_grid_flatentryentrysource) + (dst_positive_scale_grid_flatentryentrysource))) + (((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) * S ((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) + ((dst_negative_scale_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)))) + ((((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) * S ((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) + ((dst_negative_scale_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource))) + (((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) * S ((dst_negative_code_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)) + ((dst_negative_scale_grid_flatentryentrysource) + (dst_negative_scale_grid_flatentryentrysource)))))) /\ (((((exists ff_h_pvs_grid_flatentryentrysourcepositive. ff_h_pvs_grid_flatentryentrysourcepositive + S (dst_positive_grid_flatentryentrysource) = S ((S (ssr_flat_row_grid_flatentry)) * dst_positive_scale_grid_flatentryentrysource)) /\ exists ff_q_pvs_grid_flatentryentrysourcepositive. dst_positive_code_grid_flatentryentrysource = ff_q_pvs_grid_flatentryentrysourcepositive * S ((S (ssr_flat_row_grid_flatentry)) * dst_positive_scale_grid_flatentryentrysource) + (dst_positive_grid_flatentryentrysource))) /\ (((((exists ff_h_pvs_grid_flatentryentrysourcenegative. ff_h_pvs_grid_flatentryentrysourcenegative + S (dst_negative_grid_flatentryentrysource) = S ((S (ssr_flat_row_grid_flatentry)) * dst_negative_scale_grid_flatentryentrysource)) /\ exists ff_q_pvs_grid_flatentryentrysourcenegative. dst_negative_code_grid_flatentryentrysource = ff_q_pvs_grid_flatentryentrysourcenegative * S ((S (ssr_flat_row_grid_flatentry)) * dst_negative_scale_grid_flatentryentrysource) + (dst_negative_grid_flatentryentrysource))) /\ (exists ge_balance_positive_grid_flatentryentrysourcevalue ge_balance_negative_grid_flatentryentrysourcevalue. (((((ssr_entry_value_grid_flatentryentry) = 2 * (ge_balance_positive_grid_flatentryentrysourcevalue) /\ (ge_balance_negative_grid_flatentryentrysourcevalue) = 0) \/ exists ge_signed_half_grid_flatentryentrysourcevaluedecode. (((ssr_entry_value_grid_flatentryentry) = 2 * ge_signed_half_grid_flatentryentrysourcevaluedecode + 1 /\ (ge_balance_positive_grid_flatentryentrysourcevalue) = 0) /\ (ge_balance_negative_grid_flatentryentrysourcevalue) = S ge_signed_half_grid_flatentryentrysourcevaluedecode))) /\ ((dst_positive_grid_flatentryentrysource) + ge_balance_negative_grid_flatentryentrysourcevalue = (dst_negative_grid_flatentryentrysource) + ge_balance_positive_grid_flatentryentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_grid_flatentryentrymap. ff_h_pvs_grid_flatentryentrymap + S (ssr_entry_image_grid_flatentryentry) = S ((S (ssr_flat_row_grid_flatentry)) * s)) /\ exists ff_q_pvs_grid_flatentryentrymap. r = ff_q_pvs_grid_flatentryentrymap * S ((S (ssr_flat_row_grid_flatentry)) * s) + (ssr_entry_image_grid_flatentryentry))) /\ (((((ssr_flat_column_grid_flatentry)=(ssr_entry_image_grid_flatentryentry)) /\ ((ssr_prefix_value_grid_flat)=(ssr_entry_value_grid_flatentryentry)))) \/ (((~((ssr_flat_column_grid_flatentry)=(ssr_entry_image_grid_flatentryentry))) /\ ((ssr_prefix_value_grid_flat)=0)))))))))))))))
  8. 0008specialize signed_support_incidence_flat_prefix_exists (A)
  9. 0009specialize signed_support_incidence_flat_prefix_exists (r)
  10. 0010specialize signed_support_incidence_flat_prefix_exists (s)
  11. 0011specialize signed_support_incidence_flat_prefix_exists (M)
  12. 0012specialize signed_support_incidence_flat_prefix_exists (L*(S M))
  13. 0013apply signed_support_incidence_flat_prefix_exists
  14. 0014exact hA
  15. 0015cases hp
  16. 0016exists x
  17. 0017specialize signed_support_incidence_from_flat_prefix (A)
  18. 0018specialize signed_support_incidence_from_flat_prefix (r)
  19. 0019specialize signed_support_incidence_from_flat_prefix (s)
  20. 0020specialize signed_support_incidence_from_flat_prefix (L)
  21. 0021specialize signed_support_incidence_from_flat_prefix (M)
  22. 0022specialize signed_support_incidence_from_flat_prefix (x)
  23. 0023apply signed_support_incidence_from_flat_prefix
  24. 0024exact hA
  25. 0025exact hp_witness