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>on natural numbers, together with its well-foundedness proof, and then do some algebra to show that(1 + m) + n > n + m, but I can't see much evidence of the last step. And, not knowing the library definitions, I don't know which relation it is finding. $\endgroup$WellFoundedRelationis used to find a default well-founded relation for the type to the right of the=>in thetermination_byclause. The tacticdecreasing_tacticis used to actually show that the relation holds for the recursive call in question, unless this tactic is overridden by a separatedecreasing_byclause. Lean tactics are extensible with extra fallback cases. You can read more at leanprover.github.io/theorem_proving_in_lean4/… $\endgroup$