PA002J

le_add_left

Stable checked-use theorem · independently closed

Adding on the left produces an explicit order witness.

Exact expanded PA statement

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

Structural proof guide

Generated structural guide

Adding on the left produces an explicit order witness.

This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.

The proof proceeds by direct introduction and elimination.

Referenced ingredients

none

Proof neighborhood

Direct dependencies

none

Direct dependents

PA002P base_le_beta_modulus PA002Q new_value_lt_scaled_base

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.

  1. 0001intro a
  2. 0002intro b
  3. 0003exists b
  4. 0004refl