98 lines
1.4 KiB
Text
98 lines
1.4 KiB
Text
theorem ex1 : ∀ x : Int, ∃ n : Nat, n > x :=
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sorry
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theorem ex2 : ∀ x : Int, ∃ n : Nat, x > n :=
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sorry
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namespace Lt
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def ex1 (x y : Nat) (i j : Int) :=
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x < i
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def ex2 (x y : Nat) (i j : Int) :=
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i < x
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def ex3 (x y : Nat) (i j : Int) :=
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i + 1 < x
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def ex4 (x y : Nat) (i j : Int) :=
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i < x + 1
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def ex5 (x y : Nat) (i j : Int) :=
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i < x + y
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def ex6 (x y : Nat) (i j : Int) :=
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i + j < x + 0
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def ex7 (x y : Nat) (i j : Int) :=
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i + j < x + i
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def ex8 (x y : Nat) (i j : Int) :=
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i + 0 < x + i
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def ex9 (n : UInt32) :=
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n < 0xd800
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end Lt
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namespace Eq
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def ex1 (x y : Nat) (i j : Int) :=
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x = i
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def ex2 (x y : Nat) (i j : Int) :=
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i = x
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def ex3 (x y : Nat) (i j : Int) :=
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i + 1 = x
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def ex4 (x y : Nat) (i j : Int) :=
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i = x + 1
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def ex5 (x y : Nat) (i j : Int) :=
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i = x + y
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def ex6 (x y : Nat) (i j : Int) :=
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i + j = x + 0
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def ex7 (x y : Nat) (i j : Int) :=
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i + j = x + i
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def ex8 (x y : Nat) (i j : Int) :=
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i + 0 = x + i
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def ex9 (n : UInt32) :=
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n = 0xd800
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end Eq
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namespace BEq
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def ex1 (x y : Nat) (i j : Int) :=
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x == i
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def ex2 (x y : Nat) (i j : Int) :=
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i == x
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def ex3 (x y : Nat) (i j : Int) :=
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i + 1 == x
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def ex4 (x y : Nat) (i j : Int) :=
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i == x + 1
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def ex5 (x y : Nat) (i j : Int) :=
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i == x + y
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def ex6 (x y : Nat) (i j : Int) :=
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i + j == x + 0
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def ex7 (x y : Nat) (i j : Int) :=
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i + j == x + i
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def ex8 (x y : Nat) (i j : Int) :=
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i + 0 == x + i
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def ex9 (n : UInt32) :=
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n == 0xd800
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end BEq
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