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theorem proved term proof

toNat_add

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formal statement (Lean)

 261theorem toNat_add (a b : LogicNat) :
 262    toNat (a + b) = toNat a + toNat b := by

proof body

Term-mode proof.

 263  induction b with
 264  | identity =>
 265    show toNat (a + zero) = toNat a + toNat zero
 266    rw [add_zero, toNat_zero, Nat.add_zero]
 267  | step b ih =>
 268    show toNat (a + succ b) = toNat a + toNat (succ b)
 269    rw [add_succ, toNat_succ, toNat_succ, ih, Nat.add_succ]
 270
 271/-- **Recovery theorem (multiplication)**: the multiplication
 272`LogicNat` carries agrees with `Nat` multiplication under the
 273equivalence. -/

used by (14)

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depends on (11)

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