Documentation

Mathlib.Init.Classical

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.

alignments from lean 3 init.classical #

theorem Classical.axiom_of_choice {α : Sort u} {β : αSort v} {r : (x : α) → β xProp} (h : ∀ (x : α), ∃ (y : β x), r x y) :
∃ (f : (x : α) → β x), ∀ (x : α), r x (f x)

Alias of Classical.axiomOfChoice.


the axiom of choice

theorem Classical.cases_true_false (p : PropProp) (h1 : p True) (h2 : p False) (a : Prop) :
p a
theorem Classical.cases_on (a : Prop) {p : PropProp} (h1 : p True) (h2 : p False) :
p a
theorem Classical.cases {p : PropProp} (h1 : p True) (h2 : p False) (a : Prop) :
p a
theorem Classical.by_cases {p : Prop} {q : Prop} (hpq : pq) (hnpq : ¬pq) :
q

Alias of Classical.byCases.