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