Theorems · Theorem · combinatorics
Finset.cons_induction_on
∀ {α : Type u_3} {motive : Finset α → Prop} (s : Finset α),
motive ∅ → (∀ (a : α) (s : Finset α) (h : a ∉ s), motive s → motive (Finset.cons a s h)) → motive s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 58 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.
- Finsetstatement and proof · cited by 13,712
- Finset.consstatement and proof · cited by 221
- Finset.cons_inductionproof · cited by 85
Cited by37
Results whose statement or proof uses this declaration.
- Set.Finite.induction_onproof · cited by 39
- Finset.sup_lt_iffproof · cited by 23
- Finsupp.inductionproof · cited by 12
- Finset.apply_sup_eq_sup_compproof · cited by 11
- Polynomial.degree_sum_leproof · cited by 11
- map_finset_infproof · cited by 10
- map_finset_supproof · cited by 7
- Seminorm.finset_sup_applyproof · cited by 7
- Finset.gcd_eq_zero_iffproof · cited by 5
- Nat.prod_factorial_dvd_factorial_sumproof · cited by 5
- Finset.apply_inf_eq_inf_compproof · cited by 4
- MeasureTheory.integral_finsetSum_measureproof · cited by 4