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