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.
Well-foundedness of orders of well-founded relations #
Porting note: many declarations that were here in mathlib3 have been moved to Init.WF
in Lean 4 core. The ones below are all the exceptions.
theorem
PSigma.lex_wf
{α : Sort u}
{β : α → Sort v}
{r : α → α → Prop}
{s : (a : α) → β a → β a → Prop}
(ha : WellFounded r)
(hb : ∀ (x : α), WellFounded (s x))
:
WellFounded (PSigma.Lex r s)
The lexicographical order of well-founded relations is well-founded.
theorem
PSigma.revLex_wf
{α : Sort u}
{β : Sort v}
{r : α → α → Prop}
{s : β → β → Prop}
(ha : WellFounded r)
(hb : WellFounded s)
:
WellFounded (PSigma.RevLex r s)
theorem
PSigma.skipLeft_wf
(α : Type u)
{β : Type v}
{s : β → β → Prop}
(hb : WellFounded s)
:
WellFounded (PSigma.SkipLeft α s)
instance
PSigma.hasWellFounded
{α : Type u}
{β : α → Type v}
[s₁ : WellFoundedRelation α]
[s₂ : (a : α) → WellFoundedRelation (β a)]
:
Equations
- PSigma.hasWellFounded = { rel := PSigma.Lex WellFoundedRelation.rel fun (a : α) => WellFoundedRelation.rel, wf := ⋯ }