# [isabelle] Inequalities on real numbers: How to use "(x::real) > 0 --> x >= 0"?

Dear Isabelle experts,

`somewhere in a proof that involves real numbers from the theory "Real" I
``would like to infer "(x::real) >= 0" from "x > 0".
`
For now I solved the problem by introducing the following axiomatic "lemma":
lemma greater_zero_implies_greater_equal_zero [simp] :
fixes x::real
assumes "x > 0"
shows "x ≥ 0"
sorry

`(Note that I am new to Isabelle, so there might be better ways of doing
``this.)
`

`I would be interested in some built-in rule, or a theory in the library,
``that would simply do this inference for me.
`

`I am less interested in writing my own proof of this in place of the
``"sorry" above, as my overall formalisation is a higher-level applied one.
`
Cheers, and thanks in advance for any help,
Christoph
--
Christoph Lange, School of Computer Science, University of Birmingham
http://cs.bham.ac.uk/~langec, Skype duke4701
→ Building & Exploring Web Based Environments. Seville, Spain, 27 Jan–
1 Feb 2013. Deadline 2 Sep. http://iaria.org/conferences2013/WEB13.html

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