Suppose we have

type family (a :: Nat) <? (b :: Nat) :: Bool

that computes whether a is less than b, where a type checker plugin does the proof work. For some a, b, and c, if we assume (a <? b) ~ True and (b <? c) ~ True, the plugin can prove (a <? c) ~ True. However, GHC currently provides no way for the plugin to indicate that the proof of (a <? c) ~ True depends on the assumptions. This means that the plugin-produced proof evidence could potentially float out of its desired context, inviting disaster.

In term of Coercions, I propose that the PluginProv constructor of UnivCoProvenance be allowed to include a TyCoVarSet of "free variables" (that is, assumptions) in the proof. Computing the free variables of the enclosing UnivCo would returns these variables, too. It is, of course, up to the plugin to provide the right information here, but plugins generally have enough information to do this correctly (or, at least, to conservatively list all free variables of assumptions as free variables of the conclusion).