Note about Mathlib/Init/
#
The files in Mathlib/Init
are leftovers from the port from Mathlib3.
(They contain content moved from lean3 itself that Mathlib needed but was not moved to lean4.)
We intend to move all the content of these files out into the main Mathlib
directory structure.
Contributions assisting with this are appreciated.
#align
statements without corresponding declarations
(i.e. because the declaration is in Batteries or Lean) can be left here.
These will be deleted soon so will not significantly delay deleting otherwise empty Init
files.
Quot #
Some induction principles tagged with elab_as_elim
, since the attribute is missing in core.
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 functionsQuot.ind
, for theorems / proofs of propositions about quotientsQuot.recOnSubsingleton
, when the target type is aSubsingleton
Quot.hrecOn
, which usesHEq (f a) (f b)
instead of asound p ▸ f a = f b
assummption
Equations
- Quot.recOn' q f h = Quot.rec f h q
Instances For
Version of Quot.recOnSubsingleton
tagged with elab_as_elim
Equations
- Quot.recOnSubsingleton' q f = Quot.rec (fun (a : α) => f a) ⋯ q