Theorems · Theorem · number theory
Nat.digits_lt_base
∀ {b m d : ℕ}, 1 < b → d ∈ b.digits m → d < bThe digits in the base b expansion of n are all less than b, if b ≥ 2
- Defined in
- Mathlib.Data.Nat.Digits.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- Nat.digitsstatement and proof · cited by 70
- Nat.digits_lt_base'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Nat.lt_of_mem_digitsAppendproof · 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.head!_digitsproof · cited by 1
- Nat.digits_append_digitsproof · cited by 1
- Nat.self_mod_pow_eq_ofDigits_takeproof · cited by 0