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
∀ z. Primorial(0,z) → z = 1Every 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
none
0 occurrences
Exact expanded native-PA statement
forall z. (exists bpr_code_bp_zero_source bpr_scale_bp_zero_source. ((forall bpr_index_bp_zero_source_mask. (exists bpr_gap_bp_zero_source_mask_bound. bpr_gap_bp_zero_source_mask_bound + S (bpr_index_bp_zero_source_mask) = 0) -> exists bpr_value_bp_zero_source_mask. ((((exists bpr_height_bp_zero_source_mask_decoded. bpr_height_bp_zero_source_mask_decoded + S (bpr_value_bp_zero_source_mask) = S ((S (bpr_index_bp_zero_source_mask)) * bpr_scale_bp_zero_source)) /\ exists bpr_quotient_bp_zero_source_mask_decoded. bpr_code_bp_zero_source = bpr_quotient_bp_zero_source_mask_decoded * S ((S (bpr_index_bp_zero_source_mask)) * bpr_scale_bp_zero_source) + (bpr_value_bp_zero_source_mask))) /\ (((((~(S (bpr_index_bp_zero_source_mask) = 1) /\ forall bpr_left_bp_zero_source_mask_choice_prime bpr_right_bp_zero_source_mask_choice_prime. S (bpr_index_bp_zero_source_mask) = bpr_left_bp_zero_source_mask_choice_prime * bpr_right_bp_zero_source_mask_choice_prime -> bpr_left_bp_zero_source_mask_choice_prime = 1 \/ bpr_right_bp_zero_source_mask_choice_prime = 1)) /\ bpr_value_bp_zero_source_mask = S (bpr_index_bp_zero_source_mask)) \/ (~((~(S (bpr_index_bp_zero_source_mask) = 1) /\ forall bpr_left_bp_zero_source_mask_choice_prime bpr_right_bp_zero_source_mask_choice_prime. S (bpr_index_bp_zero_source_mask) = bpr_left_bp_zero_source_mask_choice_prime * bpr_right_bp_zero_source_mask_choice_prime -> bpr_left_bp_zero_source_mask_choice_prime = 1 \/ bpr_right_bp_zero_source_mask_choice_prime = 1)) /\ bpr_value_bp_zero_source_mask = 1))))) /\ (exists ff_u_bp_zero_source_product ff_v_bp_zero_source_product. ((((exists ff_h_bp_zero_source_product_start. ff_h_bp_zero_source_product_start + S (1) = S ((S (0)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_start. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_start * S ((S (0)) * ff_v_bp_zero_source_product) + (1))) /\ ((((exists ff_h_bp_zero_source_product_terminal. ff_h_bp_zero_source_product_terminal + S (z) = S ((S (0)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_terminal. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_terminal * S ((S (0)) * ff_v_bp_zero_source_product) + (z))) /\ forall ff_i_bp_zero_source_product. (exists ff_lt_bp_zero_source_product_bound. ff_lt_bp_zero_source_product_bound + S ff_i_bp_zero_source_product = 0) -> exists ff_p_bp_zero_source_product ff_r_bp_zero_source_product ff_s_bp_zero_source_product. ((((exists ff_h_bp_zero_source_product_factor. ff_h_bp_zero_source_product_factor + S (ff_p_bp_zero_source_product) = S ((S (ff_i_bp_zero_source_product)) * bpr_scale_bp_zero_source)) /\ exists ff_q_bp_zero_source_product_factor. bpr_code_bp_zero_source = ff_q_bp_zero_source_product_factor * S ((S (ff_i_bp_zero_source_product)) * bpr_scale_bp_zero_source) + (ff_p_bp_zero_source_product))) /\ ((((exists ff_h_bp_zero_source_product_partial. ff_h_bp_zero_source_product_partial + S (ff_r_bp_zero_source_product) = S ((S (ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_partial. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_partial * S ((S (ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product) + (ff_r_bp_zero_source_product))) /\ ((((exists ff_h_bp_zero_source_product_successor. ff_h_bp_zero_source_product_successor + S (ff_s_bp_zero_source_product) = S ((S (S ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_successor. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_successor * S ((S (S ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product) + (ff_s_bp_zero_source_product))) /\ ff_s_bp_zero_source_product = ff_r_bp_zero_source_product * ff_p_bp_zero_source_product)))))))) -> z = 1Proof 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.