Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
All applications
Rule | commor.sort |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~q || (q /\ s)) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || (((q /\ s) || ~q) /\ ((q /\ s) || ~s)) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(F || (q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(F || (q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(((F || q) /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ (F || s)) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || F || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~(F || q)) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ (F || (q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ (F || (q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ (((F || q) /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ (F || s)) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || F || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [0,0,1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~(F || s)) => (p /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => F || ((p /\ q) <-> (p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (F || (p /\ q)) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => ((F || p) /\ q) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ (F || q)) <-> (p /\ s)
ready: no
Rule | introfalseleft |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (F || (p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> ((F || p) /\ s)
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ (F || s))
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(((q /\ s) || ~q) /\ q /\ s) || (((q /\ s) || ~q) /\ ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(q /\ s /\ ((q /\ s) || ~s)) || (~q /\ ((q /\ s) || ~s)) => (p /\ q) <-> (p /\ s)
ready: no
Rule | logic.propositional.defequiv |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ ((q /\ s) || ~s) => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | logic.propositional.oroverand |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(q || ~q) /\ (s || ~q) /\ ((q /\ s) || ~s) => (p /\ q) <-> (p /\ s)
ready: no
Rule | logic.propositional.oroverand |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((q /\ s) || ~q) /\ (q || ~s) /\ (s || ~s) => (p /\ q) <-> (p /\ s)
ready: no