mathlib documentation

data.list.tfae

def list.tfae (l : list Prop) :
Prop

tfae: The Following (propositions) Are Equivalent.

The tfae_have and tfae_finish tactics can be useful in proofs with tfae goals.

Equations
  • l.tfae = ∀ (x : Prop), x l∀ (y : Prop), y l(x y)
theorem list.tfae_singleton (p : Prop) :
[p].tfae
theorem list.tfae_cons_of_mem {a b : Prop} {l : list Prop} (h : b l) :
(a :: l).tfae (a b) l.tfae
theorem list.tfae_cons_cons {a b : Prop} {l : list Prop} :
(a :: b :: l).tfae (a b) (b :: l).tfae
theorem list.tfae_of_forall (b : Prop) (l : list Prop) (h : ∀ (a : Prop), a l(a b)) :
theorem list.tfae_of_cycle {a b : Prop} {l : list Prop} :
list.chain (λ (_x _y : Prop), _x → _y) a (b :: l)(list.ilast' b l → a)(a :: b :: l).tfae
theorem list.tfae.out {l : list Prop} (h : l.tfae) (n₁ n₂ : ) {a b : Prop} (h₁ : l.nth n₁ = some a . "refl") (h₂ : l.nth n₂ = some b . "refl") :
a b