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 original first-admission records.
Statement with defined notation
∀ p. ∀ q. ∀ i. ∀ rb. ∀ rc. ∀ h. ∀ sh. sh = S h → (∀ x. Lt(x,sh) → ∃ y. BetaAt(rb,rc,x,y) ∧ (y = 0 ∧ (Lt(q · S i,p · S x) ∧ ¬Lt(p · S x,q · S i)) ∨ y = 1 ∧ (Lt(p · S x,q · S i) ∧ ¬Lt(q · S i,p · S x)))) → ∀ x. Lt(x,h) → ∃ y. BetaAt(rb,rc,x,y) ∧ (y = 0 ∧ (Lt(q · S i,p · S x) ∧ ¬Lt(p · S x,q · S i)) ∨ y = 1 ∧ (Lt(p · S x,q · S i) ∧ ¬Lt(q · S i,p · S x)))Every purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
12 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall p q i rb rc h sh. sh = S h -> (forall eri_column_fubini_row_restrict_source. (exists eri_gap_fubini_row_restrict_source_bound. eri_gap_fubini_row_restrict_source_bound + S (eri_column_fubini_row_restrict_source) = sh) -> exists eri_bit_fubini_row_restrict_source. ((((exists ff_h_eri_fubini_row_restrict_source_decoded. ff_h_eri_fubini_row_restrict_source_decoded + S (eri_bit_fubini_row_restrict_source) = S ((S (eri_column_fubini_row_restrict_source)) * rc)) /\ exists ff_q_eri_fubini_row_restrict_source_decoded. rb = ff_q_eri_fubini_row_restrict_source_decoded * S ((S (eri_column_fubini_row_restrict_source)) * rc) + (eri_bit_fubini_row_restrict_source))) /\ (((eri_bit_fubini_row_restrict_source = 0 /\ ((exists eri_gap_fubini_row_restrict_source_choice_left. eri_gap_fubini_row_restrict_source_choice_left + S (q * S i) = p * S eri_column_fubini_row_restrict_source) /\ ~(exists eri_gap_fubini_row_restrict_source_choice_right. eri_gap_fubini_row_restrict_source_choice_right + S (p * S eri_column_fubini_row_restrict_source) = q * S i))) \/ (eri_bit_fubini_row_restrict_source = 1 /\ ((exists eri_gap_fubini_row_restrict_source_choice_right. eri_gap_fubini_row_restrict_source_choice_right + S (p * S eri_column_fubini_row_restrict_source) = q * S i) /\ ~(exists eri_gap_fubini_row_restrict_source_choice_left. eri_gap_fubini_row_restrict_source_choice_left + S (q * S i) = p * S eri_column_fubini_row_restrict_source))))))) -> (forall eri_column_fubini_row_restrict_target. (exists eri_gap_fubini_row_restrict_target_bound. eri_gap_fubini_row_restrict_target_bound + S (eri_column_fubini_row_restrict_target) = h) -> exists eri_bit_fubini_row_restrict_target. ((((exists ff_h_eri_fubini_row_restrict_target_decoded. ff_h_eri_fubini_row_restrict_target_decoded + S (eri_bit_fubini_row_restrict_target) = S ((S (eri_column_fubini_row_restrict_target)) * rc)) /\ exists ff_q_eri_fubini_row_restrict_target_decoded. rb = ff_q_eri_fubini_row_restrict_target_decoded * S ((S (eri_column_fubini_row_restrict_target)) * rc) + (eri_bit_fubini_row_restrict_target))) /\ (((eri_bit_fubini_row_restrict_target = 0 /\ ((exists eri_gap_fubini_row_restrict_target_choice_left. eri_gap_fubini_row_restrict_target_choice_left + S (q * S i) = p * S eri_column_fubini_row_restrict_target) /\ ~(exists eri_gap_fubini_row_restrict_target_choice_right. eri_gap_fubini_row_restrict_target_choice_right + S (p * S eri_column_fubini_row_restrict_target) = q * S i))) \/ (eri_bit_fubini_row_restrict_target = 1 /\ ((exists eri_gap_fubini_row_restrict_target_choice_right. eri_gap_fubini_row_restrict_target_choice_right + S (p * S eri_column_fubini_row_restrict_target) = q * S i) /\ ~(exists eri_gap_fubini_row_restrict_target_choice_left. eri_gap_fubini_row_restrict_target_choice_left + S (q * S i) = p * S eri_column_fubini_row_restrict_target)))))))Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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.
Named ingredients (1)
01Fix variables and assumptionsL1–9
02Calculate and transport equalitiesL10–10
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L10
rewrite hsh at hprefix