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.

Lemmas about Sigma from Lean 3 core.

theorem ex_of_psig {α : Sort u} {p : α → Prop} : (x : α) ×' p x → ∃ (x : α), p x

theorem Sigma.eq {α : Type u} {β : α → Type v} {p₁ : (a : α) × β a} {p₂ : (a : α) × β a} (h₁ : p₁.fst = p₂.fst) : Eq.recOn h₁ p₁.snd = p₂.snd → p₁ = p₂

theorem PSigma.eq {α : Sort u} {β : α → Sort v} {p₁ : (a : α) ×' β a} {p₂ : (a : α) ×' β a} (h₁ : p₁.fst = p₂.fst) : Eq.recOn h₁ p₁.snd = p₂.snd → p₁ = p₂