BT0004

mul_zero_left

Stable · empty-context checked

Zero annihilates multiplication on the left.

Exact expanded PA statement

forall n. 0 * n = 0

Structural proof guide

Zero annihilates multiplication on the left.

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

Proof neighborhood

Direct dependencies

none

Direct dependents

BT0006 mul_comm BT0020 mul_eq_one_components BT0025 prime_two BT002F multiple_antisymm BT003C multiple_decidable BT003E factor_search_up_to BT003G prime_nonzero BT003K prime_divisor_exists_up_to BT0040 beta_at_self_of_bound BT006N prime_three BT0118 nonprime_has_small_prime_divisor_below_square

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]