equal
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74 later \isacom{from} clauses. In the simplest case, a fact is such a name. |
74 later \isacom{from} clauses. In the simplest case, a fact is such a name. |
75 But facts can also be composed with @{text OF} and @{text of} as shown in |
75 But facts can also be composed with @{text OF} and @{text of} as shown in |
76 \S\ref{sec:forward-proof}---hence the \dots\ in the above grammar. Note |
76 \S\ref{sec:forward-proof}---hence the \dots\ in the above grammar. Note |
77 that assumptions, intermediate \isacom{have} statements and global lemmas all |
77 that assumptions, intermediate \isacom{have} statements and global lemmas all |
78 have the same status and are thus collectively referred to as |
78 have the same status and are thus collectively referred to as |
79 \concept{facts}. |
79 \conceptidx{facts}{fact}. |
80 |
80 |
81 Fact names can stand for whole lists of facts. For example, if @{text f} is |
81 Fact names can stand for whole lists of facts. For example, if @{text f} is |
82 defined by command \isacom{fun}, @{text"f.simps"} refers to the whole list of |
82 defined by command \isacom{fun}, @{text"f.simps"} refers to the whole list of |
83 recursion equations defining @{text f}. Individual facts can be selected by |
83 recursion equations defining @{text f}. Individual facts can be selected by |
84 writing @{text"f.simps(2)"}, whole sublists by @{text"f.simps(2-4)"}. |
84 writing @{text"f.simps(2)"}, whole sublists by @{text"f.simps(2-4)"}. |
497 \begin{quote} |
497 \begin{quote} |
498 \isacom{have} \ @{text"\"x > 0\""}\\ |
498 \isacom{have} \ @{text"\"x > 0\""}\\ |
499 $\vdots$\\ |
499 $\vdots$\\ |
500 \isacom{from} @{text "`x>0`"} \dots |
500 \isacom{from} @{text "`x>0`"} \dots |
501 \end{quote} |
501 \end{quote} |
502 Note that the quotes around @{text"x>0"} are \concept{back quotes}. |
502 Note that the quotes around @{text"x>0"} are \conceptnoidx{back quotes}. |
503 They refer to the fact not by name but by value. |
503 They refer to the fact not by name but by value. |
504 |
504 |
505 \subsection{\isacom{moreover}} |
505 \subsection{\isacom{moreover}} |
506 |
506 |
507 Sometimes one needs a number of facts to enable some deduction. Of course |
507 Sometimes one needs a number of facts to enable some deduction. Of course |