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24 lines
501 B
Plaintext
24 lines
501 B
Plaintext
import NNG.MyNat.Definition
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namespace MyNat
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open MyNat
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def add : MyNat → MyNat → MyNat
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| a, 0 => a
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| a, MyNat.succ b => MyNat.succ (MyNat.add a b)
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instance : Add MyNat where
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add := MyNat.add
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/--
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This theorem proves that if you add zero to a MyNat you get back the same number.
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-/
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theorem add_zero (a : MyNat) : a + 0 = a := by rfl
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/--
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This theorem proves that (a + (d + 1)) = ((a + d) + 1) for a,d in MyNat.
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-/
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theorem add_succ (a d : MyNat) : a + (succ d) = succ (a + d) := by rfl
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