Proof for eq_four

[aleph-prover-test]

Proven lemmas: 1/1

The current goal is to prove the theorem ∀ a b c d : Nat, if a = b, a = d, and a = c, then c = b. Mathematically, this is a simple equality-transitivity/symmetry fact: since both c and b are equal to a, they must be equal to each other.

There was no need to break this into separate lemmas or sub-problems; the proof was handled directly in one step after introducing the variables and hypotheses. So the decomposition is minimal: 1 statement total, and that statement has already been solved.

Progress is therefore complete: 1 out of 1 sub-problems proved. The Lean proof rewrites c as a using a = c (in reverse), and then rewrites a as b using a = b, which immediately yields c = b.

Nothing remains to be proved for this theorem. An interesting point is that the hypothesis a = d is actually unused, which is fine: it means the conclusion follows from only two of the three equalities.