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.

Notation, basic datatypes and type classes

This file contains alignments from lean 3 init.core.

def Prod.mk.injArrow {α : Type u} {β : Type v} {x₁ : α} {y₁ : β} {x₂ : α} {y₂ : β} : (x₁, y₁) = (x₂, y₂) → ⦃P : Sort w⦄ → (x₁ = x₂ → y₁ = y₂ → P) → P

Equations

• Prod.mk.injArrow h₁ h₂ = Prod.noConfusion h₁ h₂

def PProd.mk.injArrow {α : Type u} {β : Type v} {x₁ : α} {y₁ : β} {x₂ : α} {y₂ : β} : (x₁, y₁) = (x₂, y₂) → ⦃P : Sort w⦄ → (x₁ = x₂ → y₁ = y₂ → P) → P

Equations

• PProd.mk.injArrow h₁ h₂ = Prod.noConfusion h₁ h₂

def Combinator.I {α : Sort u} (a : α) : α

Equations

• Combinator.I a = a

def Combinator.K {α : Sort u} {β : Sort v} (a : α) (_b : β) : α

Equations

• Combinator.K a _b = a

def Combinator.S {α : Sort u} {β : Sort v} {γ : Sort w} (x : α → β → γ) (y : α → β) (z : α) : γ

Equations

• Combinator.S x y z = x z (y z)