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