diff --git a/docs/bib.bib b/docs/bib.bib index db38003884989ad60c86be1638b61ed6018a5ea4..a8f88cf36dc4d36cecc3593fcfc196b49c4156af 100644 --- a/docs/bib.bib +++ b/docs/bib.bib @@ -3836,3 +3836,16 @@ year = {2013} journal={Submitted to JFP}, year = {2017}, } + +@article{Loeb, + ISSN = {00224812}, + URL = {http://www.jstor.org/stable/2266895}, + author = {Martin H. Löb}, + journal = {The Journal of Symbolic Logic}, + number = {2}, + pages = {115--118}, + publisher = {Association for Symbolic Logic}, + title = {Solution of a Problem of Leon Henkin}, + volume = {20}, + year = {1955} +} diff --git a/docs/ghost-state.tex b/docs/extended-logic.tex similarity index 99% rename from docs/ghost-state.tex rename to docs/extended-logic.tex index 7dbf916a9f9d0f1e8b8b9558acedcc1edb5e8d89..b668805abca0474014aa44d2b5b39e4817883d7f 100644 --- a/docs/ghost-state.tex +++ b/docs/extended-logic.tex @@ -41,8 +41,8 @@ We collect here some important and frequently used derived proof rules. {\TRUE \proves \plainly\TRUE} \end{mathparpagebreakable} -Noteworthy here is the fact that Löb induction can be derived from $\later$-introduction and the fact that we can take fixed-points of functions where the recursive occurrences are below $\later$.% -\footnote{See \url{https://en.wikipedia.org/wiki/L\%C3\%B6b\%27s_theorem}.} +Noteworthy here is the fact that Löb induction can be derived from $\later$-introduction and the fact that we can take fixed-points of functions where the recursive occurrences are below $\later$~\cite{Loeb}.% +\footnote{Also see \url{https://en.wikipedia.org/wiki/L\%C3\%B6b\%27s_theorem}.} Furthermore, $\TRUE \proves \plainly\TRUE$ can be derived via $\plainly$ commuting with universal quantification ranging over the empty type $0$. To derive that existential quantifiers commute with separating conjunction requires an intermediate step using a magic wand: From $P * \exists x, Q \vdash \Exists x. P * Q$ we can deduce $\Exists x. Q \vdash P \wand \Exists x. P * Q$ and then proceed via $\exists$-elimination. diff --git a/docs/iris.tex b/docs/iris.tex index 4c74119f53f99e9c967b761a3d0379561376f77f..d4c5dc8a4e9da0e7a24a25a0c6f180e47add2770 100644 --- a/docs/iris.tex +++ b/docs/iris.tex @@ -56,7 +56,7 @@ For a list of changes in Iris since then, please consult our changelog at \url{h \input{model} \endgroup \clearpage\begingroup -\input{ghost-state} +\input{extended-logic} \endgroup \clearpage\begingroup \input{language}