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
forall a b. a + b = 0 -> b = 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
0 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall a b. a + b = 0 -> b = 0Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
BT000M mul_eq_zero BT000Y le_zero BT001X add_eq_zero_left BT0020 mul_eq_one_components BT002G factor_difference BT005C bounded_beta_exclusive_recode_invariant BT005E beta_prefix_product_trace_exists BT0069 beta_factor_divides_product BT007U beta_repeat_empty BT0084 beta_range_empty BT0089 beta_prefix_sum_trace_exists BT00S0 prime_power_quotient_prefix_exists BT00SF eisenstein_initial_segment_prefix_exists BT00SH division_successor_quotient_by_bit BT00T3 beta_pascal_zero_row_exists BT00T5 beta_pascal_row_step_exists BT00T7 beta_pascal_table_prefix_exists BT00TF beta_pascal_table_diagonal_boundary BT00U0 four_power_central_recurrence_step BT00U8 primorial_factor_prefix_exists BT00US primorial_interval_factor_prefix_exists BT00XX double_quotient_carry_prefix_exists BT00YQ prime_contribution_prefix_exists BT010L prime_contribution_interval_prefix_exists BT011K prime_eighty_three BT011L prime_one_hundred_sixty_three BT011M prime_three_hundred_seventeen BT011N prime_five_hundred_twenty_one BT0127 bertrand_strictDefinition-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.
01Fix variables and assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro a
02Induction on bL2–5
03Separate the logical casesL6–6
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L6
exfalso
04Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
apply PA1
05Calculate and transport equalitiesL8–8
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L8
rewrite PA4 at h
06Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
exact h