30 lines
1,016 B
Text
30 lines
1,016 B
Text
def Xor' (a b : Prop) := (a ∧ ¬b) ∨ (b ∧ ¬a)
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@[grind =] theorem xor_def {a b : Prop} : Xor' a b ↔ (a ∧ ¬b) ∨ (b ∧ ¬a) := Iff.rfl
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class Nat.AtLeastTwo' (n : Nat) : Prop where
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prop : 2 ≤ n
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instance instNatAtLeastTwo' {n : Nat} : Nat.AtLeastTwo' (n + 2) where
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prop := Nat.succ_le_succ <| Nat.succ_le_succ <| Nat.zero_le _
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instance (priority := 100) instOfNatAtLeastTwo'
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{R : Type _} {n : Nat} [NatCast R] [Nat.AtLeastTwo' n] :
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OfNat R n where
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ofNat := n.cast
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class Distrib' (R : Type _) extends Add R where
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instance Nat.instDistrib' : Distrib' Nat where
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theorem Nat.even_xor_odd'.extracted_1_2 (k : Nat) :
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Xor'
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(@Eq.{1} Nat
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(@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
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(@instHAdd.{0} Nat (@Distrib'.toAdd.{0} Nat Nat.instDistrib'))
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(@HMul.hMul.{0, 0, 0} Nat Nat Nat
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inferInstance
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(@OfNat.ofNat.{0} Nat (nat_lit 2)
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(@instOfNatAtLeastTwo'.{0} Nat (nat_lit 2) inferInstance inferInstance)) k) 1)
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(2 * k))
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True := by grind
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