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Theorems · Theorem · order theory

LowerSet.Iic_inj

∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, LowerSet.Iic a = LowerSet.Iic b ↔ a = b
Defined in
Mathlib.Order.UpperLower.Principal
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
PartialOrder
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Around this declaration

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

LowerSet.Iic_ne_Iic · cited by 0LowerSet.Iic_ne_IicPartialOrder · cited by 6410PartialOrderLowerSet · cited by 230LowerSetLowerSet.Iic · cited by 37LowerSet.IicLowerSet.Iic_injective · cited by 1LowerSet.Iic_injectiveLowerSet.Iic_injCITED BYCITES

Cites4

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

Cited by1

Results whose statement or proof uses this declaration.