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 : BoundedOrder α) (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.

Equations
def Lattice.copy {α : Type u} (c : Lattice α) (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.

Equations
def DistribLattice.copy {α : Type u} (c : DistribLattice α) (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.

Equations
def CompleteLattice.copy {α : Type u} (c : CompleteLattice α) (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) (supₛ : Set αα) (eq_supₛ : supₛ = supₛ) (infₛ : Set αα) (eq_infₛ : infₛ = infₛ) :

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

Equations
  • One or more equations did not get rendered due to their size.
def Frame.copy {α : Type u} (c : Order.Frame α) (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) (supₛ : Set αα) (eq_supₛ : supₛ = supₛ) (infₛ : Set αα) (eq_infₛ : infₛ = infₛ) :

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

Equations
  • One or more equations did not get rendered due to their size.
def Coframe.copy {α : Type u} (c : Order.Coframe α) (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) (supₛ : Set αα) (eq_supₛ : supₛ = supₛ) (infₛ : Set αα) (eq_infₛ : infₛ = infₛ) :

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

Equations
  • One or more equations did not get rendered due to their size.
def CompleteDistribLattice.copy {α : Type u} (c : CompleteDistribLattice α) (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) (supₛ : Set αα) (eq_supₛ : supₛ = supₛ) (infₛ : Set αα) (eq_infₛ : infₛ = infₛ) :

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

Equations
  • One or more equations did not get rendered due to their size.
def ConditionallyCompleteLattice.copy {α : Type u} (c : ConditionallyCompleteLattice α) (le : ααProp) (eq_le : le = LE.le) (sup : ααα) (eq_sup : sup = Sup.sup) (inf : ααα) (eq_inf : inf = Inf.inf) (supₛ : Set αα) (eq_supₛ : supₛ = supₛ) (infₛ : Set αα) (eq_infₛ : infₛ = infₛ) :

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

Equations
  • One or more equations did not get rendered due to their size.