Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
All applications
Rule | absorpand-subset |
Location | [1,0] |
q <-> s => (p /\ q /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | command.sort |
Location | [1,0] |
q <-> s => (p /\ p /\ q /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | command.sort |
Location | [1,0,1] |
q <-> s => (p /\ p /\ q /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | compland.sort |
Location | [1,0] |
q <-> s => (p /\ p /\ q /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0] |
F || (q <-> s) => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0,0] |
(F || q) <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [0,0,1] |
q <-> (F || s) => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1] |
q <-> s => F || (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0] |
q <-> s => F || (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,0] |
q <-> s => ((F || p) /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1] |
q <-> s => (p /\ (F || (q /\ p /\ s))) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,0] |
q <-> s => (p /\ (F || q) /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1] |
q <-> s => (p /\ q /\ (F || (p /\ s))) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,0] |
q <-> s => (p /\ q /\ (F || p) /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,0,1,1,1] |
q <-> s => (p /\ q /\ p /\ (F || s)) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1] |
q <-> s => (p /\ q /\ p /\ s) || F || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0] |
q <-> s => (p /\ q /\ p /\ s) || ((F || ~(p /\ q)) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0] |
q <-> s => (p /\ q /\ p /\ s) || (~(F || (p /\ q)) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0,0] |
q <-> s => (p /\ q /\ p /\ s) || (~((F || p) /\ q) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,0,0,1] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ (F || q)) /\ ~(p /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,1] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ (F || ~(p /\ s)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(F || (p /\ s)))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,0] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~((F || p) /\ s))
ready: no
Rule | introfalseleft |
Location | [1,1,1,0,1] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ (F || s)))
ready: no
Rule | logic.propositional.defequiv |
Location | [0,0] |
(q /\ s) || (~q /\ ~s) => (p /\ q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s))
ready: no
Rule | logic.propositional.demorganand |
Location | [1,1,0] |
q <-> s => (p /\ q /\ p /\ s) || ((~p || ~q) /\ ~(p /\ s))
ready: no
Rule | logic.propositional.demorganand |
Location | [1,1,1] |
q <-> s => (p /\ q /\ p /\ s) || (~(p /\ q) /\ (~p || ~s))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || (~(p /\ q) /\ ~(p /\ s))) /\ (q || (~(p /\ q) /\ ~(p /\ s))) /\ (p || (~(p /\ q) /\ ~(p /\ s))) /\ (s || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || (~(p /\ q) /\ ~(p /\ s))) /\ (q || (~(p /\ q) /\ ~(p /\ s))) /\ ((p /\ s) || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => (p || (~(p /\ q) /\ ~(p /\ s))) /\ ((q /\ p) || (~(p /\ q) /\ ~(p /\ s))) /\ (s || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.genoroverand |
Location | [1] |
q <-> s => ((p /\ q) || (~(p /\ q) /\ ~(p /\ s))) /\ (p || (~(p /\ q) /\ ~(p /\ s))) /\ (s || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q /\ p /\ s) || ~(p /\ q)) /\ ((p /\ q /\ p /\ s) || ~(p /\ s))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => (p || (~(p /\ q) /\ ~(p /\ s))) /\ ((q /\ p /\ s) || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q) || (~(p /\ q) /\ ~(p /\ s))) /\ ((p /\ s) || (~(p /\ q) /\ ~(p /\ s)))
ready: no
Rule | logic.propositional.oroverand |
Location | [1] |
q <-> s => ((p /\ q /\ p) || (~(p /\ q) /\ ~(p /\ s))) /\ (s || (~(p /\ q) /\ ~(p /\ s)))
ready: no