Mercurial > cpdt > repo
changeset 58:1946586b9da7
First two exercises
author | Adam Chlipala <adamc@hcoop.net> |
---|---|
date | Mon, 29 Sep 2008 14:38:21 -0400 |
parents | 6f7142e082c0 |
children | 1a664ff9d2d1 |
files | src/Predicates.v |
diffstat | 1 files changed, 21 insertions(+), 0 deletions(-) [+] |
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--- a/src/Predicates.v Sun Sep 28 13:52:23 2008 -0400 +++ b/src/Predicates.v Mon Sep 29 14:38:21 2008 -0400 @@ -855,3 +855,24 @@ (* end thide *) (* end hide *) + + +(** * Exercises *) + +(** %\begin{enumerate}%#<ol># + +%\item%#<li># Prove these tautologies of propositional logic, using only the tactics [apply], [assumption], [constructor], [destruct], [intro], [intros], [left], [right], [split], and [unfold]. + %\begin{enumerate}%#<ol># + %\item%#<li># [(True \/ False) /\ (False \/ True)]#</li># + %\item%#<li># [P -> ~ ~P]#</li># + %\item%#<li># [P /\ (Q \/ R) -> (P /\ Q) \/ (P /\ R)]#</li># + #</ol> </li>#%\end{enumerate}% *) + +(** remove printing exists*) +(** %\item%#<li># Prove the following tautology of first-order logic, using only the tactics [apply], [assert], [assumption], [destruct], [eapply], [eassumption], and [exists]. You will probably find [assert] useful for stating and proving an intermediate lemma, enabling a kind of "forward reasoning," in contrast to the "backward reasoning" that is the default for Coq tactics. [eassumption] is a version of [assumption] that will do matching of unification variables. Let some variable [T] of type [Set] be the set of individuals. [x] is a constant symbol, [p] is a unary predicate symbol, [q] is a binary predicate symbol, and [f] is a unary function symbol. **) +(** printing exists $\exists$ *) +(** %\begin{enumerate}%#<ol># + %\item%#<li># [p x -> (forall x, p x -> exists y, q x y) -> (forall x y, q x y -> q y (f y)) -> exists z, q z (f z)]#</li># + #</ol> </li>#%\end{enumerate}% + +#</ol>#%\end{enumerate}% *)