# Documentation

Mathlib.Init.Quot

# Quot #

Some induction principles tagged with elab_as_elim, since the attribute is missing in core.

@[inline, reducible]
abbrev Quot.recOn' {α : Sort u} {r : ααProp} {motive : Quot rSort v} (q : Quot r) (f : (a : α) → motive (Quot.mk r a)) (h : ∀ (a b : α) (p : r a b), (_ : Quot.mk r a = Quot.mk r b)f a = f b) :
motive q

Dependent recursion principle for Quot. This constructor can be tricky to use, so you should consider the simpler versions if they apply:

• Quot.lift, for nondependent functions
• Quot.ind, for theorems / proofs of propositions about quotients
• Quot.recOnSubsingleton, when the target type is a Subsingleton
• Quot.hrecOn, which uses HEq (f a) (f b) instead of a sound p ▸ f a = f b assummption
Instances For
@[inline, reducible]
abbrev Quot.recOnSubsingleton' {α : Sort u} {r : ααProp} {motive : Quot rSort v} [h : ∀ (a : α), Subsingleton (motive (Quot.mk r a))] (q : Quot r) (f : (a : α) → motive (Quot.mk r a)) :
motive q

Version of Quot.recOnSubsingleton tagged with elab_as_elim

Instances For