Theorems · Theorem · number theory
induction_on_primes
∀ {motive : ℕ → Prop},
motive 0 → motive 1 → (∀ (p a : ℕ), Nat.Prime p → motive a → motive (p * a)) → ∀ (n : ℕ), motive n- Defined in
- Mathlib.Data.Nat.Factorization.Induction
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- Nat.recOnPrimePowproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_threeproof · cited by 2
- Nat.eq_sq_add_sq_of_isSquare_mod_neg_oneproof · cited by 1
- Nat.prime_composite_inductionproof · cited by 1
- ZMod.isSquare_neg_one_iff'proof · cited by 0