PA002R

beta_value_le_code

Stable checked-use theorem · independently closed

Every decoded beta value is at most its code.

Exact expanded PA statement

forall b c i x. ((exists h. h + S x = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + x) -> exists h. h + x = b

Structural proof guide

Generated structural guide

Every decoded beta value is at most its code.

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

The proof proceeds by case analysis (2).

Referenced ingredients

none

Proof neighborhood

Direct dependencies

none

Direct dependents

PA002T beta_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 b
  2. 0002intro c
  3. 0003intro i
  4. 0004intro x
  5. 0005intro hat
  6. 0006cases hat
  7. 0007cases hat_right
  8. 0008exists x1 * S ((S i) * c)
  9. 0009symm
  10. 0010exact hat_right_witness