18 lines
475 B
Text
18 lines
475 B
Text
theorem ex1 (n m : Nat) : 0 + (n, m).1 = n := by
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simp only
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rw [Nat.zero_add]
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theorem ex2 (n m : Nat) : 0 + (n, m).1 = n := by
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simp
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theorem ex3 (n m : Nat) : 0 + (n, m).1 + 0 = n := by
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simp only [Nat.add_zero]
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rw [Nat.zero_add]
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theorem ex4 (n m : Nat) : 0 + (n, m).1 + 0 = n := by
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simp
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theorem ex5 (m n : Nat) : m + n = n + m := by
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induction n with
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| zero => rw [Nat.zero_add, Nat.add_zero]
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| succ n ih => simp only [Nat.add_succ, Nat.succ_add, ih]
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