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71 (@{text"\<Longrightarrow>"}) and \isacom{have}/\isacom{show} introduce the conclusion. |
71 (@{text"\<Longrightarrow>"}) and \isacom{have}/\isacom{show} introduce the conclusion. |
72 |
72 |
73 Propositions are optionally named formulas. These names can be referred to in |
73 Propositions are optionally named formulas. These names can be referred to in |
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 \autoref{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 \conceptidx{facts}{fact}. |
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 |
215 above proofs (once in the statement of the lemma, once in its proof) has been |
215 above proofs (once in the statement of the lemma, once in its proof) has been |
216 eliminated. |
216 eliminated. |
217 |
217 |
218 Stating a lemma with \isacom{assumes}-\isacom{shows} implicitly introduces the |
218 Stating a lemma with \isacom{assumes}-\isacom{shows} implicitly introduces the |
219 name \indexed{@{text assms}}{assms} that stands for the list of all assumptions. You can refer |
219 name \indexed{@{text assms}}{assms} that stands for the list of all assumptions. You can refer |
220 to individual assumptions by @{text"assms(1)"}, @{text"assms(2)"}, etc.\ |
220 to individual assumptions by @{text"assms(1)"}, @{text"assms(2)"}, etc., |
221 thus obviating the need to name them individually. |
221 thus obviating the need to name them individually. |
222 |
222 |
223 \section{Proof Patterns} |
223 \section{Proof Patterns} |
224 |
224 |
225 We show a number of important basic proof patterns. Many of them arise from |
225 We show a number of important basic proof patterns. Many of them arise from |