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Table of Contents
Attribute Examples
This page contains usage examples for attributes (or directives).
of
Consider rule/theorem mp:
$\quad [|\ ?P \longrightarrow ?Q; ?P\ |] \Longrightarrow ?Q$.
Using
mp [of _ "C ∨ D"]
yields the more specific theorem
$\quad [|\ ?P \longrightarrow C \vee D; ?P\ |] \Longrightarrow C \vee D$.
Note that $C, D$ are no longer schematic variables but specific terms.
where
Consider rule/theorem mp:
$\quad [|\ ?P \longrightarrow ?Q; ?P\ |] \Longrightarrow ?Q$.
Using
mp [where Q="C ∨ D"]
yields the more specific theorem
$\quad [|\ ?P \longrightarrow C \vee D; ?P\ |] \Longrightarrow C \vee D$.
Note that $C, D$ are no longer schematic variables but specific terms.
THEN
OF
Consider rule subst:
$\quad [|\ ?s = ?t; ?P ?s\ |]\quad \Longrightarrow\quad ?P ?t$
Note that you can use this rule only to substitute from left to right, not the reverse. Using OF together with theorem sym ($?s = ?t\ \Longrightarrow\ ?t = ?s$), i.e.
subst [OF sym]
yields
$\quad [|\ ?t = ?s; ?P ?s\ |]\quad \Longrightarrow\quad ?P ?t$
which allows substitutions from right to left.