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Theorems · Theorem · order theory

OrderIso.isMax_apply

∀ {α : Type u_6} {β : Type u_7} [inst : Preorder α] [inst_1 : Preorder β] (f : α ≃o β) {x : α}, IsMax (f x) ↔ IsMax x
Defined in
Mathlib.Order.Hom.Basic
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
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Around this declaration

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

OrderIso.map_succ · cited by 4OrderIso.map_succDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderOrderIso · cited by 874OrderIsoOrderIso.symm · cited by 475OrderIso.symmIsMax · cited by 372IsMaxOrderIso.symm_apply_apply · cited by 41OrderIso.symm_apply_applyOrderIso.strictMono · cited by 26OrderIso.strictMonoStrictMono.isMax_of_apply · cited by 2StrictMono.isMax_of_applyOrderIso.isMax_applyCITED BYCITES

Cites8

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.