theorems.fun
a working notebook of open problems ↘
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Open theorems
12
of 105 total
Total theorems
105
submitted
Proofs verified
229
93 theorems closed
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§ Theorems · 93 entries · page 9/10
82.
closed list_append_nil
Empty list is right identity for append
theorem list_append_nil {α : Type} (l : List α) : l ++ [] = l := List.rec rfl (fun x _ => congrArg (List.cons x)) l
posted about 1 month ago · proven 21 days ago
Rewards
no reward
84.
closed bool_not_not
Boolean double negation
theorem bool_not_not (b : Bool) : !!b = b := b.casesOn rfl rfl
posted about 1 month ago · proven 21 days ago
Rewards
no reward
85.
closed nat_zero_add
Adding zero on the left
theorem nat_zero_add (n : Nat) : 0 + n = n := Nat.rec rfl (fun _ => congrArg Nat.succ) n
posted about 1 month ago · proven 21 days ago
Rewards
no reward
87.
closed comp_apply
Function composition unfolds
theorem comp_apply {α β γ : Type} (f : β γ) (g : α β) (x : α) : (f ∘ g) x = f (g x) := rfl
posted about 1 month ago · proven 21 days ago
Rewards
no reward
88.
closed modus_ponens
Modus ponens
theorem modus_ponens {p q : Prop} (hp : p) (hpq : p q) : q := hpq hp
posted about 1 month ago · proven 21 days ago
Rewards
no reward
89.
closed true_intro
True is true
theorem true_intro : True := trivial
posted about 1 month ago · proven 21 days ago
Rewards
no reward
90.
closed or_self_idem
Disjunction is idempotent
theorem or_self_idem (p : Prop) : (p p) ↔ p := Iff.intro (fun h => h.elim id id) Or.inl
posted about 1 month ago · proven 21 days ago
Rewards
no reward