Theorems · Theorem · number theory
Nat.factorial_succ
∀ (n : ℕ), (n + 1).factorial = (n + 1) * n.factorial
- Defined in
- Mathlib.Data.Nat.Factorial.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.factorialstatement · cited by 616
Cited by30
Results whose statement or proof uses this declaration.
- taylorWithinEval_succproof · cited by 6
- DividedPowers.factorial_mul_dpow_eq_powproof · cited by 5
- Nat.factorial_ltproof · cited by 3
- HasFPowerSeriesOnBall.factorial_smulproof · cited by 3
- Nat.add_factorial_succ_lt_factorial_add_succproof · cited by 3
- IsUnit.natCast_factorial_of_leproof · cited by 2
- Real.BohrMollerup.f_nat_eqproof · cited by 2
- Nat.add_factorial_succ_le_factorial_add_succproof · cited by 2
- iter_deriv_inv_linearproof · cited by 2
- Complex.isCauSeq_norm_expproof · cited by 2
- Nat.lt_factorial_selfproof · cited by 1
- Real.summable_pow_div_factorialproof · cited by 1