Exact expanded PA statement
forall n m. S n + m = S (n + m)Structural proof guide
A successor can move through addition on the left.
Direct prerequisites: none. The authored body proceeds by structural induction (1).
Proof neighborhood
Direct dependencies
none
Direct dependents
BT0002 add_comm BT000H drop_add_prefix_from_fixed BT000X le_succ_self BT0018 le_succ BT0019 lt_to_le BT001B lt_irrefl_expanded BT001C le_eq_or_lt BT001F lt_trans BT001K lt_not_eq_add_middle BT001O division_remainder_succ BT004J common_divisor_beta_moduli_divides_gap_times_c BT008P bit_count_bounded BT0092 factorial_succ_decompose BT00R0 ceil_div_six_shift BT00SW bertrand_h_six_step_transport_from_total BT00TL choose_symmetry BT00TM choose_positive BT00TS central_binom_succ_double_middle BT00TT choose_weighted_vertical BT00VA factorial_prime_divides_of_le BT00VH primorial_odd_interval_divides_middle BT00VJ primorial_odd_interval_le_middle BT00VK central_binom_strong_upper_step BT00VR double_half_predecessor_data BT00VS odd_positive_prefix_predecessor_bound BT00VV primorial_le_four_pow_bounded BT00XB add_lt_add BT0123 bertrand_cutoff_lt_final_primeFormal native tactic body
Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.