Theorems · Theorem · number theory
Nat.ofDigits_digits
∀ (b n : ℕ), Nat.ofDigits b (b.digits n) = n
- Defined in
- Mathlib.Data.Nat.Digits.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_commproof · cited by 1,535
- Nat.digitsstatement and proof · cited by 70
- Nat.ofDigitsstatement and proof · cited by 61
- Nat.digits_zeroproof · cited by 15
- Nat.ofDigits_singletonproof · cited by 4
- Nat.digits_add_two_add_oneproof · cited by 4
- Nat.div_lt_self'proof · cited by 3
- Nat.ofDigits_one_consproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Nat.setInvOn_digitsAppend_ofDigitsproof · cited by 3
- Nat.dvd_iff_dvd_digits_sumproof · cited by 2
- Nat.digit_sum_leproof · cited by 2
- Nat.modEq_digits_sumproof · cited by 2
- Nat.zmodeq_ofDigits_digitsproof · cited by 2
- Nat.self_div_pow_eq_ofDigits_dropproof · cited by 1
- Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digitsproof · cited by 1
- Rat.AbsoluteValue.apply_le_sum_digitsproof · cited by 1
- Nat.ofDigits_digits_append_digitsproof · cited by 1
- Nat.digits_eq_nil_iff_eq_zeroproof · cited by 1
- Nat.digits.injectiveproof · cited by 1
- Nat.head!_digitsproof · cited by 1