Commit 7f9f5dff authored by Mickael Laurent's avatar Mickael Laurent
Browse files

fix

parent 7e11b6a6
......@@ -141,7 +141,7 @@ TODO: Theorems and proof: no need for rule Inter, etc.
\\
\Infer[Proj*]
{\Gamma(x)\equiv\textstyle\bigvee_{i\in I}\pair{t_i}{s_i}\\
\forall i\in I.\ \Gamma\subst{x}{\pair{t_i}{s_i}}\vdash_\ct \ct[\pi_i x]: \{(u_j,\Gamma_j)\}_{j\in J_i}
\forall i\in I.\ \Gamma\subst{x}{\pair{t_i}{s_i}}\vdash_{[]} \ct[\pi_i x]: \{(u_j,\Gamma_j)\}_{j\in J_i}
}
{\Gamma \vdash_\ct \pi_i x: \{(u_j,\Gamma_j)\,\alt\,i\in I,\ j\in J_i\}}
{ }
......@@ -150,8 +150,8 @@ TODO: Theorems and proof: no need for rule Inter, etc.
{\Gamma(x) = t\\
t\land(\pair{\Any}{\Any})\neq\Empty\\
t\land\neg(\pair{\Any}{\Any})\neq\Empty\\
\Gamma\subst{x}{t\land(\pair{\Any}{\Any})}\vdash_\ct \ct[\pi_i x]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x}{t\land\neg(\pair{\Any}{\Any})}\vdash_\ct \ct[\pi_i x]: \{(u_j,\Gamma_j)\}_{j\in J}
\Gamma\subst{x}{t\land(\pair{\Any}{\Any})}\vdash_{[]} \ct[\pi_i x]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x}{t\land\neg(\pair{\Any}{\Any})}\vdash_{[]} \ct[\pi_i x]: \{(u_j,\Gamma_j)\}_{j\in J}
}
{\Gamma \vdash_\ct \pi_i x: \{(u_i,\Gamma_i)\}_{i\in I}\cup\{(u_j,\Gamma_j)\}_{j\in J}}
{ }
......@@ -175,7 +175,7 @@ t\land\neg(\pair{\Any}{\Any})\neq\Empty\\
\Gamma(x_1)\equiv \textstyle\bigwedge_{i\in I}\arrow {s_i}{t_i}\\
\Gamma(x_2)=s\\
s\leq \textstyle\bigvee_{i\in I}s_i\\
\forall i\in I.\ \Gamma\subst{x_2}{s\land s_i}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J_i}
\forall i\in I.\ \Gamma\subst{x_2}{s\land s_i}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J_i}
}
{ \Gamma \vdash_\ct {x_1}{x_2}: \{(u_j,\Gamma_j)\,\alt\,i\in I,\ j\in J_i\} }
{ }
......@@ -185,23 +185,23 @@ t\land\neg(\pair{\Any}{\Any})\neq\Empty\\
\Gamma(x_1)\equiv \textstyle\bigwedge_{i\in I}\arrow {s_i}{t_i}\\
s_\circ=\textstyle\bigvee_{i\in I}s_i\\
\Gamma(x_2)=s\\s\land s_\circ\neq\Empty\\s\land \neg s_\circ\neq\Empty\\
\Gamma\subst{x_2}{s\land s_\circ}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x_2}{s\land \neg s_\circ}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
\Gamma\subst{x_2}{s\land s_\circ}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x_2}{s\land \neg s_\circ}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
}
{ \Gamma \vdash_\ct {x_1}{x_2}: \{(u_i,\Gamma_i)\}_{i\in I}\cup\{(u_j,\Gamma_j)\}_{j\in J} }
{ }
\\
\Infer[AppL*]
{\Gamma(x_1)\equiv\textstyle\bigvee_{i\in I}t_i\leq\arrow{\Empty}{\Any}\\
\forall i\in I.\ \Gamma\subst{x_1}{t_i}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J_i}
\forall i\in I.\ \Gamma\subst{x_1}{t_i}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J_i}
}
{\Gamma \vdash_\ct {x_1}{x_2}: \{(u_j,\Gamma_j)\,\alt\,i\in I,\ j\in J_i\}}
{ }
\\
\Infer[AppLDom]
{\Gamma(x_1) = t\\t\land (\arrow{\Empty}{\Any})\neq\Empty\\t\land \neg (\arrow{\Empty}{\Any})\neq\Empty\\
\Gamma\subst{x_1}{t\land(\arrow{\Empty}{\Any})}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x_1}{t\land\neg(\arrow{\Empty}{\Any})}\vdash_\ct \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
\Gamma\subst{x_1}{t\land(\arrow{\Empty}{\Any})}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x_1}{t\land\neg(\arrow{\Empty}{\Any})}\vdash_{[]} \ct[{x_1}{x_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
}
{\Gamma \vdash_\ct {x_1}{x_2}: \{(u_i,\Gamma_i)\}_{i\in I}\cup\{(u_j,\Gamma_j)\}_{j\in J}}
{ }
......@@ -224,8 +224,8 @@ t\land\neg(\pair{\Any}{\Any})\neq\Empty\\
\\
\Infer[Case*]
{\Gamma(x) = t_\circ\\
\Gamma\subst{x}{t_\circ\land t}\vdash_\ct \ct[\tcase {x} t {e_1}{e_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x}{t_\circ\land\neg t}\vdash_\ct \ct[\tcase {x} t {e_1}{e_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
\Gamma\subst{x}{t_\circ\land t}\vdash_{[]} \ct[\tcase {x} t {e_1}{e_2}]: \{(u_i,\Gamma_i)\}_{i\in I}\\
\Gamma\subst{x}{t_\circ\land\neg t}\vdash_{[]} \ct[\tcase {x} t {e_1}{e_2}]: \{(u_j,\Gamma_j)\}_{j\in J}
}
{\Gamma\vdash_\ct \tcase {x} t {e_1}{e_2}: \{(u_i,\Gamma_i)\}_{i\in I}\cup\{(u_j,\Gamma_j)\}_{j\in J}}
{ }
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment