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--import Mathlib.Tactic.Basic
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--import Mathlib.Tactic.Cases
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/-- Our copy of the natural numbers called `MyNat`. -/
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inductive MyNat where
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| zero : MyNat
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| succ : MyNat → MyNat
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deriving BEq, DecidableEq, Inhabited
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@[inherit_doc]
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notation "ℕ" => MyNat
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-- Note: as long as we do not import `Mathlib.Init.Data.Nat.Notation` this is fine.
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namespace MyNat
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instance : Inhabited MyNat where
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default := MyNat.zero
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def myNatFromNat (x : Nat) : MyNat :=
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match x with
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| Nat.zero => MyNat.zero
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| Nat.succ b => MyNat.succ (myNatFromNat b)
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def natFromMyNat (x : MyNat) : Nat :=
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match x with
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| MyNat.zero => Nat.zero
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| MyNat.succ b => Nat.succ (natFromMyNat b)
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instance ofNat {n : Nat} : OfNat MyNat n where
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ofNat := myNatFromNat n
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instance : ToString MyNat where
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toString p := toString (natFromMyNat p)
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theorem zero_eq_0 : MyNat.zero = 0 := rfl
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def one : MyNat := MyNat.succ 0
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