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chore(order/omega_complete_partial_order): clean up references (#7781)
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fix the references rendering by adding them to the .bib
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YaelDillies committed Jun 2, 2021
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66 changes: 49 additions & 17 deletions docs/references.bib
Expand Up @@ -120,21 +120,20 @@ @InProceedings{ beylin1996
isbn = "978-3-540-70722-6"
}

@book {billingsley1999,
AUTHOR = {Billingsley, Patrick},
TITLE = {Convergence of probability measures},
SERIES = {Wiley Series in Probability and Statistics: Probability and
Statistics},
EDITION = {Second},
NOTE = {A Wiley-Interscience Publication},
PUBLISHER = {John Wiley \& Sons, Inc., New York},
YEAR = {1999},
PAGES = {x+277},
ISBN = {0-471-19745-9},
MRCLASS = {60B10 (28A33 60F17)},
MRNUMBER = {1700749},
DOI = {10.1002/9780470316962},
URL = {https://doi.org/10.1002/9780470316962},
@Book { billingsley1999,
author = {Billingsley, Patrick},
title = {Convergence of probability measures},
series = {Wiley Series in Probability and Statistics: Probability and Statistics},
edition = {Second},
note = {A Wiley-Interscience Publication},
publisher = {John Wiley \& Sons, Inc., New York},
year = {1999},
pages = {x+277},
isbn = {0-471-19745-9},
mrclass = {60B10 (28A33 60F17)},
mrnumber = {1700749},
doi = {10.1002/9780470316962},
url = {https://doi.org/10.1002/9780470316962},
}

@Book{ borceux-vol1,
Expand Down Expand Up @@ -196,6 +195,18 @@ @Book{ bourbaki1975b
mrnumber = {2109105}
}

@Article{ cadiou1972,
title = {Recursive definitions of partial functions and their computations},
doi = {10.1145/942580.807072},
number = {14},
journal = {ACM SIGACT News},
author = {Cadiou, Jean Marie Cadiou and Manna, Zohar},
year = {1972},
month = {Jan},
pages = {58–65}
}


@Book{ calugareanu,
author = {C\v{a}lug\v{a}reanu, Grigore},
year = {2000},
Expand Down Expand Up @@ -385,8 +396,7 @@ @InProceedings{ Gallier2011Notes

@Article{ ghys87:groupes,
author = {Étienne Ghys},
title = {Groupes d'homeomorphismes du cercle et cohomologie
bornee},
title = {Groupes d'homéomorphismes du cercle et cohomologie bornée},
journal = {Contemporary Mathematics},
year = 1987,
volume = 58,
Expand Down Expand Up @@ -423,6 +433,15 @@ @Book{ Gratzer2011
mrnumber = {2768581}
}

@Book{ gunter1992,
title = {Semantics of Programming Languages: Structures and Techniques},
isbn = {0262570955},
publisher = {MIT Press},
author = {Gunter, Carl A.},
year = {1992}
}


@Article{ Gusakov2021,
author = {Alena Gusakov and Bhavik Mehta and Kyle A. Miller},
title = {Formalizing Hall's Marriage Theorem in Lean},
Expand Down Expand Up @@ -621,6 +640,19 @@ @Book{ marcus1977number
publisher = {Springer}
}

@article{ markowsky1976,
title = {Chain-complete posets and directed sets with applications},
volume = {6},
DOI = {10.1007/bf02485815},
number = {1},
journal = {Algebra Universalis},
author = {Markowsky, George},
year = {1976},
month = {Dec},
pages = {53–68}
}


@InProceedings{ mcbride1996,
title = {Inverting inductively defined relations in {LEGO}},
author = {McBride, Conor},
Expand Down
10 changes: 5 additions & 5 deletions src/order/omega_complete_partial_order.lean
Expand Up @@ -46,9 +46,9 @@ supremum helps define the meaning of recursive procedures.
## References
* [G. Markowsky, *Chain-complete posets and directed sets with applications*, https://doi.org/10.1007/BF02485815][markowsky]
* [J. M. Cadiou and Zohar Manna, *Recursive definitions of partial functions and their computations.*, https://doi.org/10.1145/942580.807072][cadiou]
* [Carl A. Gunter, *Semantics of Programming Languages: Structures and Techniques*, ISBN: 0262570955][gunter]
* [Chain-complete posets and directed sets with applications][markowsky1976]
* [Recursive definitions of partial functions and their computations][cadiou1972]
* [Semantics of Programming Languages: Structures and Techniques][gunter1992]
-/

universes u v
Expand Down Expand Up @@ -119,7 +119,7 @@ namespace omega_complete_partial_order

/-- A chain is a monotonically increasing sequence.
See the definition on page 114 of [gunter]. -/
See the definition on page 114 of [gunter1992]. -/
def chain (α : Type u) [preorder α] :=
ℕ →ₘ α

Expand Down Expand Up @@ -188,7 +188,7 @@ operation on increasing sequences indexed by natural numbers (which we
call `ωSup`). In this sense, it is strictly weaker than join complete
semi-lattices as only ω-sized totally ordered sets have a supremum.
See the definition on page 114 of [gunter]. -/
See the definition on page 114 of [gunter1992]. -/
class omega_complete_partial_order (α : Type*) extends partial_order α :=
(ωSup : chain α → α)
(le_ωSup : ∀(c:chain α), ∀ i, c i ≤ ωSup c)
Expand Down

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