23 lines
1.1 KiB
Text
23 lines
1.1 KiB
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: bracket
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Assumed: bracket_eq
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not_false : (¬ ⊥) = ⊤
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not_true : (¬ ⊤) = ⊥
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Nat::mul_comm : ∀ a b : ℕ, a * b = b * a
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Nat::add_assoc : ∀ a b c : ℕ, a + b + c = a + (b + c)
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Nat::add_comm : ∀ a b : ℕ, a + b = b + a
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Nat::add_zeror : ∀ a : ℕ, a + 0 = a
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forall_rem [check] : ∀ (A : TypeU) (H : inhabited A) (p : Bool), (A → p) ↔ p
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eq_id : ∀ (A : (Type U)) (a : A), a = a ↔ ⊤
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exists_rem : ∀ (A : TypeU) (H : inhabited A) (p : Bool), (∃ x : A, p) ↔ p
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exists_and_distributel : ∀ (A : TypeU) (p : Bool) (φ : A → Bool),
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(∃ x : A, φ x ∧ p) ↔ (∃ x : A, φ x) ∧ p
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exists_or_distribute : ∀ (A : TypeU) (φ ψ : A → Bool),
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(∃ x : A, φ x ∨ ψ x) ↔ (∃ x : A, φ x) ∨ (∃ x : A, ψ x)
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not_and : ∀ a b : Bool, ¬ (a ∧ b) ↔ ¬ a ∨ ¬ b
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not_neq : ∀ (A : TypeU) (a b : A), ¬ a ≠ b ↔ a = b
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not_true : (¬ ⊤) = ⊥
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and_comm : ∀ a b : Bool, a ∧ b ↔ b ∧ a
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and_truer : ∀ a : Bool, a ∧ ⊤ ↔ a
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bracket_eq [check] : ∀ a : Bool, bracket a = a
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