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Theorems · Theorem · order theory

UpperSet.lt_erase

∀ {α : Type u_1} [inst : Preorder α] {s : UpperSet α} {a : α}, s < s.erase a ↔ a ∈ s
Defined in
Mathlib.Order.UpperLower.Closure
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UpperSet.infIrred_iff_of_finite · cited by 1UpperSet.infIrred_iff_of_…Preorder · cited by 7952PreorderUpperSet · cited by 245UpperSetIff.not_left · cited by 49Iff.not_leftLE.le.lt_iff_ne' · cited by 16le.lt_iff_ne'UpperSet.erase · cited by 9UpperSet.eraseUpperSet.le_erase · cited by 1UpperSet.le_eraseUpperSet.erase_eq · cited by 1UpperSet.erase_eqUpperSet.lt_eraseCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.