Exact expanded PA statement
forall a b c d. a = b -> c = d -> a + c = b + dStructural proof guide
Generated structural guide
Addition preserves equality in both arguments.
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
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.