BT0009

one_mul

Stable · empty-context checked

One is a left identity for multiplication.

Exact expanded PA statement

forall n. 1 * n = n

Structural proof guide

One is a left identity for multiplication.

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

Proof neighborhood

Direct dependencies

none

Direct dependents

BT0020 mul_eq_one_components BT0027 one_multiple BT0039 gauss_coprime_cancel BT0055 le_scaled_nonzero BT005E beta_prefix_product_trace_exists BT0089 beta_prefix_sum_trace_exists BT0093 pow_one_from_zero_successor BT00PX le_mul_of_one_le_left BT00U2 central_binom_four_weighted_of_recurrence BT00VM central_binom_strong_upper_of_laws BT00YF division_three_scaled_upper_of_quotient_lt BT011N prime_five_hundred_twenty_one BT0122 bertrand_cover_three_hundred_seventeen_five_hundred_twenty_one

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]