English
Copy construction for a Coframe preserving co-operations including sdiff.
Русский
Копирование кофрейм сохраняет ко-операции, включая sdiff
LaTeX
$$$\\exists c' : \\text{Coframe }\\alpha \\text{ with preserved data } le, top, bot, sup, inf, sdiff, hnot, sSup, sInf$$$
Lean4
/-- A function to create a provable equal copy of a coframe with possibly different definitional
equalities. -/
def 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 : Max α).max) (inf : α → α → α)
(eq_inf : inf = (by infer_instance : Min α).min) (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
where
toCompleteLattice :=
CompleteLattice.copy (@Coframe.toCompleteLattice α c) le eq_le top eq_top bot eq_bot sup eq_sup inf eq_inf sSup
eq_sSup sInf eq_sInf
__ :=
CoheytingAlgebra.copy (@Coframe.toCoheytingAlgebra α c) le eq_le top eq_top bot eq_bot sup eq_sup inf eq_inf sdiff
eq_sdiff hnot eq_hnot
