BT0000

zero_add

Stable · empty-context checked

Zero is a left identity for addition; unlike PA3, this needs induction.

Exact expanded PA statement

forall n. 0 + n = n

Structural proof guide

Zero is a left identity for addition; unlike PA3, this needs induction.

Direct prerequisites: none. The authored body proceeds by structural induction (1).

Proof neighborhood

Direct dependencies

none

Direct dependents

BT0002 add_comm BT000A mul_one BT000E le_refl BT000H drop_add_prefix_from_fixed BT000X le_succ_self BT001C le_eq_or_lt BT001O division_remainder_succ BT001U division_remainder_unique BT002G factor_difference BT0034 gcd_balanced_bezout_exists_up_to BT0040 beta_at_self_of_bound BT0046 dvd_to_mod_zero BT004F binary_crt BT004J common_divisor_beta_moduli_divides_gap_times_c BT0092 factorial_succ_decompose BT00QH power_valuation_successor_not_divides BT00R1 ceil_div_six_total BT00RA floor_sqrt_total BT00SA prime_power_quotient_tail_zero BT00SS prime_power_quotient_prefix_last_zero BT00TL choose_symmetry BT00TT choose_weighted_vertical BT00VA factorial_prime_divides_of_le BT00VK central_binom_strong_upper_step BT00X0 floor_sqrt_factorized_threshold_thirty_two BT00XF division_zero_quotient_of_lt BT00XQ power_quotient_prefix_sum_extend_zero BT00YC double_quotient_carry_prefix_entries_zero BT0126 bertrand_upper_endpoint_factorization

Formal native tactic body

Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.

  1. 0001induction n
  2. 0002simp
  3. 0003simp [IH]