Theorems · Theorem · number theory
Nat.cast_descFactorial_two
∀ (S : Type u_1) [inst : Ring S] (a : ℕ), ↑(a.descFactorial 2) = ↑a * (↑a - 1)
Convenience lemma. The a - 1 is not using truncated subtraction, as opposed to the definition
of Nat.descFactorial as a natural.
- Defined in
- Mathlib.Data.Nat.Factorial.Cast
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- mul_negproof · cited by 590
- Nat.cast_addproof · cited by 586
- neg_zeroproof · cited by 542
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- zero_subproof · cited by 335
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_choose_twoproof · cited by 1