English
binaryRec' zero bit (Nat.bit b n) equals bit b n h (binaryRec' zero bit n).
Русский
binaryRec' ноль bit (Nat.bit b n) равно bit b n h (binaryRec' ноль bit n).
LaTeX
$$$ binaryRec'\ zero\ bit\ (Nat.bit\ b\ n) = bit\ b\ n\ h\ (binaryRec'\ zero\ bit\ n) $$$
Lean4
@[simp]
theorem binaryRec'_one (zero : motive 0)
(bit : (b : Bool) → (n : Nat) → (n = 0 → b = true) → motive n → motive (n.bit b)) :
binaryRec' (motive := motive) zero bit 1 = bit true 0 (by simp) zero := by
rw [binaryRec', Nat.binaryRec_one, dif_pos]