Re: [isabelle] the minimum of a set



> This was what I suspected first, but 
> 
> 	have "\<not>({x. P(x)} = {})" by auto
> 
> gives successfully: 
> 
> 	have {x. P(x)} ~= {}

Even then you need finiteness to proceed, e.g.:

  fix P :: "'a::linorder => bool"
  have "{x. P x} ~= {}" sorry
  then obtain x xs where "{x. P x} = insert x xs" by blast
  moreover have "finite xs" sorry
  ultimately have "Min {x. P x} <= x" by auto


Hope this helps
	Florian
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