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Theorems · Theorem · order theory

ChainCompletePartialOrder.map_mem_bot

∀ {α : Type u_1} [inst : ChainCompletePartialOrder α] {x : α} {f : α → α} {y : α},
  (∀ (x : α), x ≤ f x) → y ∈ ChainCompletePartialOrder.bot x f → f y ∈ ChainCompletePartialOrder.bot x f
Defined in
Mathlib.Order.BourbakiWitt
Cited by
2 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ChainCompletePartialOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ChainCompletePartialOrder.IsExtremePt.bot_eq_of_le_or_map_le · cited by 2IsExtremePt.bot_eq_of_le_…ChainCompletePartialOrder.IsExtremePt.setOfPred_isExtremePt_isAdmissible · cited by 2IsExtremePt.setOfPred_isE…Set · cited by 53352SetSet.mem_image_of_mem · cited by 371Set.mem_image_of_memChainCompletePartialOrder · cited by 19ChainCompletePartialOrderChainCompletePartialOrder.bot · cited by 12ChainCompletePartialOrder…ChainCompletePartialOrder.bot_isAdmissible · cited by 4ChainCompletePartialOrder…ChainCompletePartialOrder.IsAdmissible.image_self_subset_self · cited by 3IsAdmissible.image_self_s…ChainCompletePartialOrder.map…CITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.