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Theorems · Theorem · order theory

CovBy.ge_of_gt

∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, b ⋖ a → b < c → a ≤ c
Defined in
Mathlib.Order.Cover
Cited by
6 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

Order.IsNormal.map_isSuccLimit · cited by 4IsNormal.map_isSuccLimitcovBy_iff_lt_iff_le_right · cited by 2covBy_iff_lt_iff_le_rightcountable_setOfPred_covBy_left · cited by 2countable_setOfPred_covBy…IsLUB.isSuccPrelimit_of_notMem · cited by 2IsLUB.isSuccPrelimit_of_n…CovBy.Ioo_eq_Ico · cited by 1CovBy.Ioo_eq_IcoCovBy.unique_right · cited by 0CovBy.unique_rightLinearOrder · cited by 8572LinearOrderCovBy · cited by 290CovByCovBy.wcovBy · cited by 15CovBy.wcovByWCovBy.ge_of_gt · cited by 1WCovBy.ge_of_gtCovBy.ge_of_gtCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.