PA002S

le_add_right

Stable checked-use theorem · independently closed

Adding on the right produces an explicit order witness.

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 a b. exists k. k + a = a + b

Structural proof guide

Generated structural guide

Adding on the right produces an explicit order witness.

Use the direct prerequisites add_comm as previously established PA formulas.

The proof proceeds by direct introduction and elimination.

Referenced ingredients

PA000F add_comm

Proof neighborhood

Direct dependencies

PA000F add_comm

Direct dependents

PA002T beta_value_lt_scaled_base PA00DR odd_half_division_quotient_bounded

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.

Read the argument

Proof checkpoints

4 script commands · 3 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.

Named ingredients (1)
add comm
01Fix variables and assumptionsL1–2

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro a
  2. L2
    intro b
02Construct an explicit witnessL3–3

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

  1. L3
    exists b
03Use earlier factsL4–4

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L4
    apply add_comm

Library-wide reading audit

Original exact command ledger · 4 lines
  1. 0001intro a
  2. 0002intro b
  3. 0003exists b
  4. 0004apply add_comm