diff --git a/spec/changelog.tex b/spec/changelog.tex index 3ff625899a52be0c1bec08067343ef10d3e84903..e2e3410e98459ff17fa943cffce008f907bc9655 100644 --- a/spec/changelog.tex +++ b/spec/changelog.tex @@ -7,6 +7,10 @@ Proof rules: \proofRule{bitblast_ult}. \item Addition of rules \proofRule{la_mult_pos} and \proofRule{la_mult_neg} to describe multiplication with a positive or negative factor. \item Addition of rules \proofRule{symm} and \proofRule{not_symm} to express symmetry of equality explicitly. + \item Addition of the rule \proofRule{eq_symmetric} to express symmetry + of equality explicitly but as an equivalence. Note that in principle this + could be done with the rule \proofRule{symm} above, but would require a long + and tedious use of \proofRule{subproof} for each direction of the equivalence. \end{itemize} \noindent @@ -47,9 +51,9 @@ command. Beyond many smaller clarifications and typographic improvements, the following changes are implemented in this release. \begin{itemize} - \item Add an abstract proof checking procedure to clarify - the semantics of the proof format. - \item Add a description of the semantics of contexts based on λ-terms. + \item Add an abstract proof checking procedure to clarify + the semantics of the proof format. + \item Add a description of the semantics of contexts based on λ-terms. \item List all transformations that are implicit in Alethe proofs. \item Change the notation used for terms from first-order style (e.g., $f(x,g(y))$) to higher-order style (e.g., diff --git a/spec/rule_list.tex b/spec/rule_list.tex index 2d707d17c05ca3380a78e89352174e39d4811b28..257f36ac3c122d70404b50bb39f03804ee07e453 100644 --- a/spec/rule_list.tex +++ b/spec/rule_list.tex @@ -1774,6 +1774,17 @@ See \proofRule{symm} for an explanation of this rule. \end{RuleDescription} +\begin{RuleDescription}{eq_symmetric} +\begin{AletheX} +$i$. & \ctxsep & $ (t_1 ≈ t_2) ≈ (t_2 ≈ t_1)$ & (\currule) \\ +\end{AletheX} + +\noindent +Note that since Alethe allows the implicit reordering of equalities, this +rule is technically superfluous. However, the rule is useful to state +an explicit usage of symmetry of equality reasoning to aid proof reconstruction. +\end{RuleDescription} + \clearpage \subsection{Index of Rules} \label{sec:alethe:rules-index}