Elimination with a Motive

I present a tactic, BasicElim, for Type Theory based proof systems to apply elimination rules in a reenement setting. Applicable rules are parametric in their conclusion, expressing the leverage hypotheses ~ x yield on any ~ x we choose. represents the motive for an elimination: BasicElim's job is to construct a suited to the goal at hand. If these ~ x inhabit an instance of 's domain, I adopt a technique standard in`folklore', generalizing the ~ x and expressing the restriction by equation. A novel notion of = readily permits dependent equations, and a second tactic, Unify, simpiies the equational hypotheses thus appearing in subgoals. Given such technology, it becomes eeective to express properties of datatypes, relations and functions in this style. A small extension couples BasicElim with rewriting, allowing complex techniques to be packaged in a single rule.