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