# Documentation

Mathlib.Order.Copy

# Tooling to make copies of lattice structures #

Sometimes it is useful to make a copy of a lattice structure where one replaces the data parts with provably equal definitions that have better definitional properties.

def BoundedOrder.copy {α : Type u} {h : LE α} {h' : LE α} (c : ) (top : α) (eq_top : top = ) (bot : α) (eq_bot : bot = ) (le_eq : ∀ (x y : α), x y x y) :

A function to create a provable equal copy of a bounded order with possibly different definitional equalities.

Instances For
def Lattice.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) :

A function to create a provable equal copy of a lattice with possibly different definitional equalities.

Instances For
def DistribLattice.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) :

A function to create a provable equal copy of a distributive lattice with possibly different definitional equalities.

Instances For
def CompleteLattice.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (top : α) (eq_top : top = ) (bot : α) (eq_bot : bot = ) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (sSup : Set αα) (eq_sSup : sSup = sSup) (sInf : Set αα) (eq_sInf : sInf = sInf) :

A function to create a provable equal copy of a complete lattice with possibly different definitional equalities.

Instances For
def Frame.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (top : α) (eq_top : top = ) (bot : α) (eq_bot : bot = ) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (sSup : Set αα) (eq_sSup : sSup = sSup) (sInf : Set αα) (eq_sInf : sInf = sInf) :

A function to create a provable equal copy of a frame with possibly different definitional equalities.

Instances For
def Coframe.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (top : α) (eq_top : top = ) (bot : α) (eq_bot : bot = ) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (sSup : Set αα) (eq_sSup : sSup = sSup) (sInf : Set αα) (eq_sInf : sInf = sInf) :

A function to create a provable equal copy of a coframe with possibly different definitional equalities.

Instances For
def CompleteDistribLattice.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (top : α) (eq_top : top = ) (bot : α) (eq_bot : bot = ) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (sSup : Set αα) (eq_sSup : sSup = sSup) (sInf : Set αα) (eq_sInf : sInf = sInf) :

A function to create a provable equal copy of a complete distributive lattice with possibly different definitional equalities.

Instances For
def ConditionallyCompleteLattice.copy {α : Type u} (c : ) (le : ααProp) (eq_le : le = LE.le) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (sSup : Set αα) (eq_sSup : sSup = sSup) (sInf : Set αα) (eq_sInf : sInf = sInf) :

A function to create a provable equal copy of a conditionally complete lattice with possibly different definitional equalities.

Instances For