Theorems · Theorem · order theory

GaloisConnection.l_bot

∀ {α : Type u} {β : Type v} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : OrderBot α] [inst_3 : OrderBot β]
  {u : α → β} {l : β → α}, GaloisConnection l u → l ⊥ = ⊥

Defined in

Mathlib.Order.GaloisConnection.Defs

Cited by

63 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

PartialOrderPreorderOrderBotOrderBot