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