Proof for eq_four - #208
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Proven lemmas: 1/1
The 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 very straightforward equality-chaining fact: since c = a and a = b, it follows by transitivity that c = b.
There was no need to split this into multiple sub-problems, because the statement can be handled directly after introducing the variables and hypotheses. So the proof consists of a single step of reasoning using symmetry on a = c to get c = a, and then transitivity with a = b.
Progress is complete: 1 out of 1 proof obligations has been solved. Nothing remains to be proved.
An interesting point is that the hypothesis a = d is actually unused, so the theorem is stronger than necessary. The Lean proof uses the compact argument hac.symm.trans hab, which exactly expresses “from c = a and a = b, conclude c = b.”