BT0004

mul_zero_left

Stable checked-use theorem · independently kernel verified

Zero annihilates multiplication on the left.

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.

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 the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.

Read the argument

Proof checkpoints

3 script commands · 1 reading checkpoints · 0 local claims

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.

01Induction on nL1–3

Split the argument into the base and successor obligations. The induction hypothesis is available only in the successor branch.

  1. L1
    induction n
  2. L2
    simp
  3. L3
    simp [IH]

Library-wide reading audit

Original exact command ledger · 3 lines
  1. 0001induction n
  2. 0002simp
  3. 0003simp [IH]