File: Mathlib/Order/Copy.lean

full_name: OrderTop.copy
code: /-- A function to create a provable equal copy of a top order
with possibly different definitional equalities. -/
def OrderTop.copy {h : LE α} {h' : LE α} (c : @OrderTop α h')
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (le_eq : ∀ x y : α, (@LE.le α h) x y ↔ x ≤ y) : @OrderTop α h 
goal: OrderTop α

full_name: OrderBot.copy
code: /-- A function to create a provable equal copy of a bottom order
with possibly different definitional equalities. -/
def OrderBot.copy {h : LE α} {h' : LE α} (c : @OrderBot α h')
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (le_eq : ∀ x y : α, (@LE.le α h) x y ↔ x ≤ y) : @OrderBot α h 
goal: OrderBot α

full_name: BoundedOrder.copy
code: /-- A function to create a provable equal copy of a bounded order
with possibly different definitional equalities. -/
def BoundedOrder.copy {h : LE α} {h' : LE α} (c : @BoundedOrder α h')
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (le_eq : ∀ x y : α, (@LE.le α h) x y ↔ x ≤ y) : @BoundedOrder α h 
goal: BoundedOrder α

full_name: Lattice.copy
code: /-- A function to create a provable equal copy of a lattice
with possibly different definitional equalities. -/
def Lattice.copy (c : Lattice α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf) : Lattice α 
goal: Lattice α

full_name: DistribLattice.copy
code: /-- A function to create a provable equal copy of a distributive lattice
with possibly different definitional equalities. -/
def DistribLattice.copy (c : DistribLattice α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf) : DistribLattice α 
goal: DistribLattice α

full_name: GeneralizedHeytingAlgebra.copy
code: /-- A function to create a provable equal copy of a generalised heyting algebra
with possibly different definitional equalities. -/
def GeneralizedHeytingAlgebra.copy (c : GeneralizedHeytingAlgebra α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (himp : α → α → α) (eq_himp : himp = (by infer_instance : HImp α).himp) :
    GeneralizedHeytingAlgebra α 
goal: GeneralizedHeytingAlgebra α

full_name: GeneralizedCoheytingAlgebra.copy
code: /-- A function to create a provable equal copy of a generalised coheyting algebra
with possibly different definitional equalities. -/
def GeneralizedCoheytingAlgebra.copy (c : GeneralizedCoheytingAlgebra α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sdiff : α → α → α) (eq_sdiff : sdiff = (by infer_instance : SDiff α).sdiff) :
    GeneralizedCoheytingAlgebra α 
goal: GeneralizedCoheytingAlgebra α

full_name: HeytingAlgebra.copy
code: /-- A function to create a provable equal copy of a heyting algebra
with possibly different definitional equalities. -/
def HeytingAlgebra.copy (c : HeytingAlgebra α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (himp : α → α → α) (eq_himp : himp = (by infer_instance : HImp α).himp)
    (compl : α → α) (eq_compl : compl = (by infer_instance : HasCompl α).compl) :
    HeytingAlgebra α 
goal: HeytingAlgebra α

full_name: CoheytingAlgebra.copy
code: /-- A function to create a provable equal copy of a coheyting algebra
with possibly different definitional equalities. -/
def CoheytingAlgebra.copy (c : CoheytingAlgebra α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sdiff : α → α → α) (eq_sdiff : sdiff = (by infer_instance : SDiff α).sdiff)
    (hnot : α → α) (eq_hnot : hnot = (by infer_instance : HNot α).hnot) :
    CoheytingAlgebra α 
goal: CoheytingAlgebra α

full_name: BiheytingAlgebra.copy
code: /-- A function to create a provable equal copy of a biheyting algebra
with possibly different definitional equalities. -/
def BiheytingAlgebra.copy (c : BiheytingAlgebra α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sdiff : α → α → α) (eq_sdiff : sdiff = (by infer_instance : SDiff α).sdiff)
    (hnot : α → α) (eq_hnot : hnot = (by infer_instance : HNot α).hnot)
    (himp : α → α → α) (eq_himp : himp = (by infer_instance : HImp α).himp)
    (compl : α → α) (eq_compl : compl = (by infer_instance : HasCompl α).compl) :
    BiheytingAlgebra α 
goal: BiheytingAlgebra α

full_name: CompleteLattice.copy
code: /-- A function to create a provable equal copy of a complete lattice
with possibly different definitional equalities. -/
def CompleteLattice.copy (c : CompleteLattice α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sSup : Set α → α) (eq_sSup : sSup = (by infer_instance : SupSet α).sSup)
    (sInf : Set α → α) (eq_sInf : sInf = (by infer_instance : InfSet α).sInf) :
    CompleteLattice α 
goal: CompleteLattice α

full_name: Frame.copy
code: /-- A function to create a provable equal copy of a frame with possibly different definitional
equalities. -/
def Frame.copy (c : Frame α) (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (himp : α → α → α) (eq_himp : himp = (by infer_instance : HImp α).himp)
    (compl : α → α) (eq_compl : compl = (by infer_instance : HasCompl α).compl)
    (sSup : Set α → α) (eq_sSup : sSup = (by infer_instance : SupSet α).sSup)
    (sInf : Set α → α) (eq_sInf : sInf = (by infer_instance : InfSet α).sInf) : Frame α 
goal: Order.Frame α

full_name: Coframe.copy
code: /-- A function to create a provable equal copy of a coframe with possibly different definitional
equalities. -/
def Coframe.copy (c : Coframe α) (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sdiff : α → α → α) (eq_sdiff : sdiff = (by infer_instance : SDiff α).sdiff)
    (hnot : α → α) (eq_hnot : hnot = (by infer_instance : HNot α).hnot)
    (sSup : Set α → α) (eq_sSup : sSup = (by infer_instance : SupSet α).sSup)
    (sInf : Set α → α) (eq_sInf : sInf = (by infer_instance : InfSet α).sInf) : Coframe α 
goal: Order.Coframe α

full_name: CompleteDistribLattice.copy
code: /-- A function to create a provable equal copy of a complete distributive lattice
with possibly different definitional equalities. -/
def CompleteDistribLattice.copy (c : CompleteDistribLattice α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (top : α) (eq_top : top = (by infer_instance : Top α).top)
    (bot : α) (eq_bot : bot = (by infer_instance : Bot α).bot)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sdiff : α → α → α) (eq_sdiff : sdiff = (by infer_instance : SDiff α).sdiff)
    (hnot : α → α) (eq_hnot : hnot = (by infer_instance : HNot α).hnot)
    (himp : α → α → α) (eq_himp : himp = (by infer_instance : HImp α).himp)
    (compl : α → α) (eq_compl : compl = (by infer_instance : HasCompl α).compl)
    (sSup : Set α → α) (eq_sSup : sSup = (by infer_instance : SupSet α).sSup)
    (sInf : Set α → α) (eq_sInf : sInf = (by infer_instance : InfSet α).sInf) :
    CompleteDistribLattice α 
goal: CompleteDistribLattice α

full_name: ConditionallyCompleteLattice.copy
code: /-- A function to create a provable equal copy of a conditionally complete lattice
with possibly different definitional equalities. -/
def ConditionallyCompleteLattice.copy (c : ConditionallyCompleteLattice α)
    (le : α → α → Prop) (eq_le : le = (by infer_instance : LE α).le)
    (sup : α → α → α) (eq_sup : sup = (by infer_instance : Sup α).sup)
    (inf : α → α → α) (eq_inf : inf = (by infer_instance : Inf α).inf)
    (sSup : Set α → α) (eq_sSup : sSup = (by infer_instance : SupSet α).sSup)
    (sInf : Set α → α) (eq_sInf : sInf = (by infer_instance : InfSet α).sInf) :
    ConditionallyCompleteLattice α 
goal: ConditionallyCompleteLattice α