Theorems · Theorem · combinatorics
Finset.Colex.erase_le_erase
∀ {α : Type u_1} [inst : PartialOrder α] {s : Finset α} {a b : α} [inst_1 : DecidableEq α],
a ∈ s → b ∈ s → (toColex (s.erase a) ≤ toColex (s.erase b) ↔ b ≤ a)- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Equivstatement · cited by 8,337
- PartialOrderstatement and proof · cited by 6,410
- eq_or_neproof · cited by 1,117
- Finset.erasestatement and proof · cited by 455
- Colexstatement · cited by 131
- toColexstatement and proof · cited by 90
- Finset.Colex.toColex_sdiff_le_toColex_sdiff'proof · cited by 2
- Finset.Colex.singleton_le_singletonproof · cited by 2
- Finset.erase_sdiff_eraseproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.Colex.erase_le_erase_min'proof · cited by 1
- Finset.Colex.erase_lt_eraseproof · cited by 0