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Theorems · Theorem · order theory

InitialSeg.le_iff_le

∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder β] {a a' : α} [inst_1 : PartialOrder α] (f : α ≤i β),
  f a ≤ f a' ↔ a ≤ a'
Defined in
Mathlib.Order.InitialSeg
Cited by
4 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPartialOrder
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Around this declaration

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

Cardinal.lift_le · cited by 78Cardinal.lift_leInitialSeg.le_apply_iff · cited by 3InitialSeg.le_apply_iffInitialSeg.isMin_apply_iff · cited by 2InitialSeg.isMin_apply_iffPrincipalSeg.le_iff_le · cited by 1PrincipalSeg.le_iff_leDFunLike.coe · cited by 62936DFunLike.coePartialOrder · cited by 6410PartialOrderInitialSeg · cited by 70InitialSegOrderEmbedding.le_iff_le · cited by 32OrderEmbedding.le_iff_leInitialSeg.toOrderEmbedding · cited by 8InitialSeg.toOrderEmbeddi…InitialSeg.le_iff_leCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.