Extension of reassoc to isomorphisms. #
We extend reassoc and reassoc_of% for equality of isomorphisms.
Adding @[reassoc] to a lemma named F of shape ∀ .., f = g,
where f g : X ≅ Y in some category will create a new lemma named F_assoc of shape
∀ .. {Z : C} (h : Y ≅ Z), f ≪≫ h = g ≪≫ h
but with the conclusions simplified using basic proportions in isomorphisms in a category
(Iso.trans_refl, Iso.refl_trans, Iso.trans_assoc, Iso.trans_symm,
Iso.symm_self_id and Iso.self_symm_id).
This is useful for generating lemmas which the simplifier can use even on expressions that are already right associated.
Simplify an expression using only the axioms of a groupoid.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Given an equation f = g between isomorphisms X ≅ Y in a category,
produce the equation ∀ {Z} (h : Y ≅ Z), f ≪≫ h = g ≪≫ h,
but with compositions fully right associated, identities removed, and functors applied.
Equations
- One or more equations did not get rendered due to their size.