whats the standard way of stating that some sets partition another

Question

I would write {1, 2} + {3} + {4} = {1, 2, 3, 4} in maths to say that the sets on LHS partition that of RHS. Is there something similar in isabelle so I don't need to go through all the permutations {1, 2} intersect {3} = {} etc.

[EDIT]

I've found this disjoint definition in the probability sigma algebra package but is there anything that wouldn't introduce that dependency?

score 1 · Accepted Answer · answered Jul 16 '15 at 06:01

1

disjoint is probably the best choice. You can just copy the definition and the few lemmas after it to your own theory.

I will talk to Johannes Hölzl (who made the Probability Theory library) and ask him what he thinks about moving disjoint into HOL so that it is available with no extra imports.

answered Jul 16 '15 at 06:01

Manuel Eberl

7,858
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Thanks, that's a great idea! – simonzack Jul 16 '15 at 06:05

score 1 · Answer 2 · answered Jul 16 '15 at 09:15

1

In the development version of Isabelle (http://isabelle.in.tum.de/repos/isabelle/rev/53697011b03a) it is now in its own theory file:

~~/src/HOL/Library/Disjoint_Sets

answered Jul 16 '15 at 09:15

Johannes

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whats the standard way of stating that some sets partition another

2 Answers2