diff options
| author | narboux | 2004-03-26 16:56:54 +0000 |
|---|---|---|
| committer | narboux | 2004-03-26 16:56:54 +0000 |
| commit | c46d7e23b0a0a30439f70e9379fd3764e86f9fd0 (patch) | |
| tree | 7d7a811502c974326460a5529fbe0596c9f6eef9 | |
| parent | 09868acc09f646c5501df88aa6bf30f6e4e83800 (diff) | |
*** empty log message ***
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8514 85f007b7-540e-0410-9357-904b9bb8a0f7
| -rw-r--r-- | doc/newfaq/main.tex | 44 |
1 files changed, 22 insertions, 22 deletions
diff --git a/doc/newfaq/main.tex b/doc/newfaq/main.tex index c77b948675..2eddaa202e 100644 --- a/doc/newfaq/main.tex +++ b/doc/newfaq/main.tex @@ -220,26 +220,26 @@ Windows. The sources can be easily adapted to all platforms supporting Objective \Question[conjonction]{My goal is a conjunction, how can I prove it ?} Use some theorem or assumption or use the {\tt split} tactic. -\begin{coq_example*} +\begin{coq_example} Goal forall A B:Prop, A->B-> A/\B. intros. split. assumption. assumption. Qed. -\end{coq_example*} +\end{coq_example} \Question[conjonctionhyp]{My goal contains a conjunction as an hypothesis, how can I use it ?} If you want to decompose your hypohtesis into other hypothesis you can use the {\tt decompose} tactic : -\begin{coq_example*} +\begin{coq_example} Goal forall A B:Prop, A/\B-> B. intros. decompose [and] H. assumption. Qed. -\end{coq_example*} +\end{coq_example} \Question[disjonction]{My goal is a disjonction, how can I prove it ?} @@ -249,13 +249,13 @@ You can prove the left part or the right part of the disjunction using reasoning step, use {\tt } to prove the right part with the assumption that the left part of the disjunction is false. -\begin{coq_example*} +\begin{coq_example} Goal forall A B:Prop, A-> A\/B. intros. left. assumption. Qed. -\end{coq_example*} +\end{coq_example} @@ -274,12 +274,12 @@ Use some theorem or assumption or exhibits the witness using {\tt exists} tactic \Question[taut]{My goal is a propositional tautology, how can I prove it ?} Just use the {\tt tauto} tactic. -\begin{coq_example*} +\begin{coq_example} Goal forall A B:Prop, A-> A\/B. intros. tauto. Qed. -\end{coq_example*} +\end{coq_example} \Question[firstorder]{My goal is a first order formula, how can I prove it ?} @@ -290,30 +290,30 @@ Just use the {\tt firstorder} tactic. \Question[cong]{My goal is solvable by a sequence of rewrites, how can I prove it ?} Just use the {\tt congruence} tactic. -\begin{coq_example*} +\begin{coq_example} Goal forall a b c d e, a=d -> b=e -> c+b=d -> c+e=a. intros. congruence. Qed. -\end{coq_example*} +\end{coq_example} \Question[congnot]{My goal is disequality solvable by a sequence of rewrites, how can I prove it ?} Just use the {\tt congruence} tactic. -%\begin{coq_example*} +%\begin{coq_example} %Goal forall a b c d, a<>d -> b=a -> d=c+b -> b<>c+b. %intros. %congruence. %Qed. -%\end{coq_example*} +%\end{coq_example} \Question[ring]{My goal is an equality on some ring (e.g. natural numbers), how can I prove it ?} Just use the {\tt ring} tactic. -\begin{coq_example*} +\begin{coq_example} Require Import ZArith. Require Ring. Open Local Scope Z_scope. @@ -321,13 +321,13 @@ Goal forall a b : Z, (a+b)*(a+b) = a*a + 2*a*b + b*b. intros. ring. Qed. -\end{coq_example*} +\end{coq_example} \Question[field]{My goal is an equality on some field (e.g. reals), how can I prove it ?} Just use the {\tt field} tactic. -\begin{coq_example*} +\begin{coq_example} Require Import Reals. Require Ring. Open Local Scope R_scope. @@ -336,13 +336,13 @@ intros. field. assumption. Qed. -\end{coq_example*} +\end{coq_example} \Question[omega]{My goal is an inequality on R, how can I prove it ?} -%\begin{coq_example*} +%\begin{coq_example} %Require Import ZArith. %Require Omega. %Open Local Scope Z_scope. @@ -350,7 +350,7 @@ Qed. %intros. %omega. %Qed. -%\end{coq_example*} +%\end{coq_example} \Question[gb]{My goal is an equation solvable using equational hypothesis on some ring (e.g. natural numbers), how can I prove it ?} @@ -361,7 +361,7 @@ Just use the {\tt gb} tactic. Just use the {\tt apply} tactic. -\begin{coq_example*} +\begin{coq_example} Lemma mylemma : forall x, x+0 = x. auto. Qed. @@ -369,7 +369,7 @@ Qed. Goal 3+0 = 3. apply mylemma. Qed. -\end{coq_example*} +\end{coq_example} \Question[autowith]{My goal is solvable by some lemma within a set of lemmas and I don't want to remember which one, how can I prove it ?} @@ -379,12 +379,12 @@ Use a base of Hints. Use the {\tt assumption} tactic. -\begin{coq_example*} +\begin{coq_example} Goal 1=1 -> 1=1. intro. assumption. Qed. -\end{coq_example*} +\end{coq_example} \Question[trivial]{My goal is ???, how can I prove it ?} |
