BT011W

bertrand_cover_thirteen_twenty_three

Alpha v34 checked-use theorem · independently kernel and Lean verified; not Stable

The checked finite cover inequality from 13 to 23.

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

exists bpr_le_gap_bb8c_thirteen_twenty_three. bpr_le_gap_bb8c_thirteen_twenty_three + (23) = (13 + 13)

Structural proof guide

The checked finite cover inequality from 13 to 23.

Direct prerequisites: none. The authored body proceeds by closed numeral normalization (1).

Proof neighborhood

Direct dependencies

none

Direct dependents

BT0124 bertrand_small_closed_upper

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

2 script commands · 2 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.

01Construct an explicit witnessL1–1

Supply the displayed value, then prove that it has the required property.

  1. L1
    exists 3
02Calculate and transport equalitiesL2–2

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L2
    norm_num

Library-wide reading audit

Original exact command ledger · 2 lines
  1. 0001exists 3
  2. 0002norm_num