Mathlib Map

Theorems · Definition · order theory

ChainCompletePartialOrder.bot

{α : Type u_1} → [ChainCompletePartialOrder α] → α → (α → α) → Set α

The bottom admissible set with base point x and inflationary function f

Defined in
Mathlib.Order.BourbakiWitt
Cited by
12 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ChainCompletePartialOrder

Around this declaration

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

ChainCompletePartialOrder.bot_isAdmissible · cited by 4ChainCompletePartialOrder…ChainCompletePartialOrder.IsExtremePt.mem_bot · cited by 3IsExtremePt.mem_botChainCompletePartialOrder.IsExtremePt.map_le_of_mem_of_lt · cited by 2IsExtremePt.map_le_of_mem…ChainCompletePartialOrder.IsExtremePt.setOfPred_isExtremePt_eq_bot · cited by 2IsExtremePt.setOfPred_isE…ChainCompletePartialOrder.IsExtremePt.setOfPred_isExtremePt_isAdmissible · cited by 2IsExtremePt.setOfPred_isE…ChainCompletePartialOrder.map_mem_bot · cited by 2ChainCompletePartialOrder…ChainCompletePartialOrder.subset_bot_iff · cited by 2ChainCompletePartialOrder…ChainCompletePartialOrder.IsExtremePt.bot_eq_of_le_or_map_le · cited by 2IsExtremePt.bot_eq_of_le_…ChainCompletePartialOrder.IsExtremePt.mem_bot_iff_isExtremePt · cited by 1IsExtremePt.mem_bot_iff_i…ChainCompletePartialOrder.IsExtremePt.bot_isChain · cited by 1IsExtremePt.bot_isChainChainCompletePartialOrder.IsExtremePt.recOn · cited by 0IsExtremePt.recOnChainCompletePartialOrder.IsExtremePt.setOf_isExtremePt_eq_bot · cited by 0IsExtremePt.setOf_isExtre…ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary · cited by 0ChainCompletePartialOrder…ChainCompletePartialOrder.IsExtremePt.casesOn · cited by 0IsExtremePt.casesOnSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredSet.sInter · cited by 225Set.sInterChainCompletePartialOrder · cited by 19ChainCompletePartialOrderChainCompletePartialOrder.IsAdmissible · cited by 8ChainCompletePartialOrder…ChainCompletePartialOrder.botCITED BYCITES

Cites5

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

Cited by14

Results whose statement or proof uses this declaration.