Equivalence induction says that in order to prove something for all equivalences, it is enough to prove it for all identity equivalences for all types.--This follows from univalence. But also, conversely, univalence follows from it:Is this known? Some years ago it was claimed in this list that equivalence induction would be strictly weaker than univalence.To prove the above, I apply a technique I learned from Peter Lumsdaine, that given an abstract identity system (Id, refl , J) with no given "computation rule" for J, produces another identity system (Id, refl , J' , J'-comp) witha "propositional computation rule" J'-comp for J'.Martin
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