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data.​list.​tfae

data.​list.​tfae

source
list.​tfae
list.​tfae.​out
list.​tfae_cons_cons
list.​tfae_cons_of_mem
list.​tfae_nil
list.​tfae_of_cycle
list.​tfae_of_forall
list.​tfae_singleton
source
def list.​tfae  :
list Prop → Prop

Equations
  • l.tfae = ∀ (x : Prop), x ∈ l → ∀ (y : Prop), y ∈ l → (x ↔ y)
source
theorem list.​tfae_nil  :
list.nil.tfae

source
theorem list.​tfae_singleton (p : Prop) :
[p].tfae

source
theorem list.​tfae_cons_of_mem {a b : Prop} {l : list Prop} :
b ∈ l → ((a :: l).tfae ↔ (a ↔ b) ∧ l.tfae)

source
theorem list.​tfae_cons_cons {a b : Prop} {l : list Prop} :
(a :: b :: l).tfae ↔ (a ↔ b) ∧ (b :: l).tfae

source
theorem list.​tfae_of_forall (b : Prop) (l : list Prop) :
(∀ (a : Prop), a ∈ l → (a ↔ b)) → l.tfae

source
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

source
theorem list.​tfae.​out {l : list Prop} (h : l.tfae) (n₁ n₂ : ℕ) {a b : Prop} :
(l.nth n₁ = option.some a . "refl") → (l.nth n₂ = option.some b . "refl") → (a ↔ b)

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