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sav08:proof_rule_for_equality [2008/04/02 19:22] vkuncak |
sav08:proof_rule_for_equality [2008/04/02 22:53] vkuncak |
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{subst(\sigma)(D \cup C[t])} | {subst(\sigma)(D \cup C[t])} | ||
\] | \] | ||
- | where $\sigma$ is mgu of $\{s,s'\}$. | + | where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. |
+ | |||
+ | Here $C[s']$ means that $s'$ occurs somewhere in $C$; then $C[t]$ results from replacing that occurrence of $s'$ with $t$. | ||
=== Equality Resolution === | === Equality Resolution === | ||
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\[ | \[ | ||
\frac{C \cup \{ s \neq s' \}} | \frac{C \cup \{ s \neq s' \}} | ||
- | {C} | + | {subst(\sigma)(C)} |
\] | \] | ||
- | where $\sigma$ is mgu of $\{s,s'\}$. | + | where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. |