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 || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | command.sort |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p /\ (~p || q)) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || ((~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
F || ((~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((F || ~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((F || ~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~(F || p) || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || F || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ (F || ~p)) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~(F || p)) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || F || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((F || ~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((F || ~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~(F || p) || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || F || q) /\ r) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [0,0,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ (F || r)) => p -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => F || (p -> (q /\ r))
ready: no
Rule | introfalseleft |
Location | [1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => (F || p) -> (q /\ r)
ready: no
Rule | introfalseleft |
Location | [1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (F || (q /\ r))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => p -> ((F || q) /\ r)
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => p -> (q /\ (F || r))
ready: no
Rule | logic.propositional.absorpand |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
~p || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(~p /\ ~p) || (q /\ ~p) || ((~p || q) /\ r) => p -> (q /\ r)
ready: no
Rule | logic.propositional.andoveror |
Location | [0,0,1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || (~p /\ r) || (q /\ r) => p -> (q /\ r)
ready: no
Rule | logic.propositional.defimpl |
Location | [1] |
![](http://ideas.cs.uu.nl/images/external.png)
((~p || q) /\ ~p) || ((~p || q) /\ r) => ~p || (q /\ r)
ready: no
Rule | logic.propositional.oroverand |
Location | [0,0] |
![](http://ideas.cs.uu.nl/images/external.png)
(((~p || q) /\ ~p) || ~p || q) /\ (((~p || q) /\ ~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 || q) /\ r)) /\ (~p || ((~p || q) /\ r)) => p -> (q /\ r)
ready: no