Theorems · Theorem · combinatorics
Finset.Colex.lt_iff_exists_forall_lt
∀ {α : Type u_1} [inst : LinearOrder α] {s t : Colex (Finset α)},
s < t ↔ ∃ a ∈ ofColex t, a ∉ ofColex s ∧ ∀ b ∈ ofColex s, b ∉ ofColex t → b < a- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Colexstatement and proof · cited by 131
- ofColexstatement · cited by 51
- Finset.Colex.toColex_lt_toColex_iff_exists_forall_ltproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.geomSum_ofColex_strictMonoproof · cited by 2
- Finset.Colex.erase_le_erase_min'proof · cited by 1