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.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.defimpl |
Location | [1,0,0] |
![](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.defimpl |
Location | [1,0,1] |
![](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.defimpl |
Location | [1,1,0,0] |
![](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.defimpl |
Location | [1,1,1,0] |
![](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.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