diff options
Diffstat (limited to 'test/phase7')
| -rw-r--r-- | test/phase7/concurrent-earlier.tex | 11 | ||||
| -rw-r--r-- | test/phase7/concurrent-failure-root.tex | 10 | ||||
| -rw-r--r-- | test/phase7/concurrent-later.tex | 11 | ||||
| -rw-r--r-- | test/phase7/dependent-proof-chain.tex | 11 | ||||
| -rw-r--r-- | test/phase7/diamond-base.tex | 3 | ||||
| -rw-r--r-- | test/phase7/diamond-left.tex | 5 | ||||
| -rw-r--r-- | test/phase7/diamond-right.tex | 5 | ||||
| -rw-r--r-- | test/phase7/diamond-root.tex | 6 | ||||
| -rw-r--r-- | test/phase7/structure-obligation-batch.tex | 16 |
9 files changed, 78 insertions, 0 deletions
diff --git a/test/phase7/concurrent-earlier.tex b/test/phase7/concurrent-earlier.tex new file mode 100644 index 0000000..a6548f6 --- /dev/null +++ b/test/phase7/concurrent-earlier.tex @@ -0,0 +1,11 @@ +\begin{axiom}\label{phase7_concurrent_earlier_axiom} + For all $x$ we have $x = x$. +\end{axiom} + +\begin{proposition}\label{phase7_concurrent_earlier_failure} + For all $x$ we have $x = x$. +\end{proposition} +\begin{proof} + Fix $x$. + Follows by assumption. +\end{proof} diff --git a/test/phase7/concurrent-failure-root.tex b/test/phase7/concurrent-failure-root.tex new file mode 100644 index 0000000..7c23e6e --- /dev/null +++ b/test/phase7/concurrent-failure-root.tex @@ -0,0 +1,10 @@ +\import{test/phase7/concurrent-earlier.tex} +\import{test/phase7/concurrent-later.tex} + +\begin{proposition}\label{phase7_concurrent_unstarted_root} + For all $x$ we have $x = x$. +\end{proposition} +\begin{proof} + Fix $x$. + Follows by assumption. +\end{proof} diff --git a/test/phase7/concurrent-later.tex b/test/phase7/concurrent-later.tex new file mode 100644 index 0000000..2daf8e9 --- /dev/null +++ b/test/phase7/concurrent-later.tex @@ -0,0 +1,11 @@ +\begin{axiom}\label{phase7_concurrent_later_axiom} + For all $x$ we have $x = x$. +\end{axiom} + +\begin{proposition}\label{phase7_concurrent_later_failure} + For all $x$ we have $x = x$. +\end{proposition} +\begin{proof} + Fix $x$. + Follows by assumption. +\end{proof} diff --git a/test/phase7/dependent-proof-chain.tex b/test/phase7/dependent-proof-chain.tex new file mode 100644 index 0000000..3d70f47 --- /dev/null +++ b/test/phase7/dependent-proof-chain.tex @@ -0,0 +1,11 @@ +\begin{proposition}\label{phase7_dependent_proof} + For all $x$ we have $x = x$. +\end{proposition} +\begin{proof} + Fix $x$. + Show $x = x$. + \begin{subproof} + Follows by assumption. + \end{subproof} + Follows by assumption. +\end{proof} diff --git a/test/phase7/diamond-base.tex b/test/phase7/diamond-base.tex new file mode 100644 index 0000000..5814596 --- /dev/null +++ b/test/phase7/diamond-base.tex @@ -0,0 +1,3 @@ +\begin{proposition}\label{phase7_diamond_base} + For all $x$ we have $x = x$. +\end{proposition} diff --git a/test/phase7/diamond-left.tex b/test/phase7/diamond-left.tex new file mode 100644 index 0000000..863b0fe --- /dev/null +++ b/test/phase7/diamond-left.tex @@ -0,0 +1,5 @@ +\import{test/phase7/diamond-base.tex} + +\begin{proposition}\label{phase7_diamond_left} + For all $x$ we have $x = x$. +\end{proposition} diff --git a/test/phase7/diamond-right.tex b/test/phase7/diamond-right.tex new file mode 100644 index 0000000..0a6a955 --- /dev/null +++ b/test/phase7/diamond-right.tex @@ -0,0 +1,5 @@ +\import{test/phase7/diamond-base.tex} + +\begin{proposition}\label{phase7_diamond_right} + For all $x$ we have $x = x$. +\end{proposition} diff --git a/test/phase7/diamond-root.tex b/test/phase7/diamond-root.tex new file mode 100644 index 0000000..523102a --- /dev/null +++ b/test/phase7/diamond-root.tex @@ -0,0 +1,6 @@ +\import{test/phase7/diamond-left.tex} +\import{test/phase7/diamond-right.tex} + +\begin{proposition}\label{phase7_diamond_root} + For all $x$ we have $x = x$. +\end{proposition} diff --git a/test/phase7/structure-obligation-batch.tex b/test/phase7/structure-obligation-batch.tex new file mode 100644 index 0000000..c71d6cd --- /dev/null +++ b/test/phase7/structure-obligation-batch.tex @@ -0,0 +1,16 @@ +\begin{axiom}\label{phase7_batch_prefix} + $\emptyset = \emptyset$. +\end{axiom} + +\begin{struct}\label{phase7_batch_structure} + A phase seven batch structure $X$ is a onesorted structure equipped with + \begin{enumerate} + \item $\phaseSevenPick$ + \end{enumerate} + such that + \begin{enumerate} + \item\label{phase7_batch_first} $X = X$. + \item\label{phase7_batch_second} + $\phaseSevenPick[X] = \phaseSevenPick[X]$. + \end{enumerate} +\end{struct} |
