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
∀ b. ∀ c. ∀ l. ∀ n. l = 0 → BitCount(b,c,l,n) → n = 0Every purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
Definitions used by this theorem
In the theorem statement
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall b c l n. l = 0 -> (((exists ff_u_zero_sum ff_v_zero_sum. ((((exists ff_h_zero_sum_start. ff_h_zero_sum_start + S (0) = S ((S (0)) * ff_v_zero_sum)) /\ exists ff_q_zero_sum_start. ff_u_zero_sum = ff_q_zero_sum_start * S ((S (0)) * ff_v_zero_sum) + (0))) /\ ((((exists ff_h_zero_sum_terminal. ff_h_zero_sum_terminal + S (n) = S ((S (l)) * ff_v_zero_sum)) /\ exists ff_q_zero_sum_terminal. ff_u_zero_sum = ff_q_zero_sum_terminal * S ((S (l)) * ff_v_zero_sum) + (n))) /\ forall ff_i_zero_sum. (exists ff_lt_zero_sum_bound. ff_lt_zero_sum_bound + S ff_i_zero_sum = l) -> exists ff_a_zero_sum ff_r_zero_sum ff_s_zero_sum. ((((exists ff_h_zero_sum_summand. ff_h_zero_sum_summand + S (ff_a_zero_sum) = S ((S (ff_i_zero_sum)) * c)) /\ exists ff_q_zero_sum_summand. b = ff_q_zero_sum_summand * S ((S (ff_i_zero_sum)) * c) + (ff_a_zero_sum))) /\ ((((exists ff_h_zero_sum_partial. ff_h_zero_sum_partial + S (ff_r_zero_sum) = S ((S (ff_i_zero_sum)) * ff_v_zero_sum)) /\ exists ff_q_zero_sum_partial. ff_u_zero_sum = ff_q_zero_sum_partial * S ((S (ff_i_zero_sum)) * ff_v_zero_sum) + (ff_r_zero_sum))) /\ ((((exists ff_h_zero_sum_successor. ff_h_zero_sum_successor + S (ff_s_zero_sum) = S ((S (S ff_i_zero_sum)) * ff_v_zero_sum)) /\ exists ff_q_zero_sum_successor. ff_u_zero_sum = ff_q_zero_sum_successor * S ((S (S ff_i_zero_sum)) * ff_v_zero_sum) + (ff_s_zero_sum))) /\ ff_s_zero_sum = ff_r_zero_sum + ff_a_zero_sum)))))) /\ (forall ff_i_zero_bits. (exists ff_lt_zero_bits_bound. ff_lt_zero_bits_bound + S ff_i_zero_bits = l) -> exists ff_bit_zero_bits. ((((exists ff_h_zero_bits_decoded. ff_h_zero_bits_decoded + S (ff_bit_zero_bits) = S ((S (ff_i_zero_bits)) * c)) /\ exists ff_q_zero_bits_decoded. b = ff_q_zero_bits_decoded * S ((S (ff_i_zero_bits)) * c) + (ff_bit_zero_bits))) /\ (ff_bit_zero_bits = 0 \/ ff_bit_zero_bits = 1))))) -> n = 0Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
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 assumptionsL1–6
02Calculate and transport equalitiesL7–9
03Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
cases hcount
Original defined command ledger · 15 lines
- 0001
intro b - 0002
intro c - 0003
intro l - 0004
intro n - 0005
intro hl - 0006
intro hcount - 0007
rewrite hl at hcount - 0008
rewrite hl at hcount - 0009
rewrite hl at hcount - 0010
cases hcount - 0011
specialize beta_sum_zero b - 0012
specialize beta_sum_zero c - 0013
specialize beta_sum_zero n - 0014
apply beta_sum_zero - 0015
exact hcount_left