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theorem proved term proof

toNat_fromNat

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formal statement (Lean)

 243theorem toNat_fromNat : ∀ n : Nat, toNat (fromNat n) = n := by

proof body

Term-mode proof.

 244  intro n
 245  induction n with
 246  | zero => rfl
 247  | succ n ih =>
 248    show toNat (fromNat (Nat.succ n)) = Nat.succ n
 249    rw [fromNat_succ, toNat_succ, ih]
 250
 251/-- **Recovery theorem (carrier)**: `LogicNat` and `Nat` have the same
 252underlying set, witnessed by the round-trip equalities. -/

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