# Re: [isabelle] a simplifier question 2

On 07.06.2015 01:30, noam neer wrote:
[simplifier questions]
The simplifier performs (primarily) rewriting. A term t will be
rewritten with an equation s = s' if there is some substitution of the
variables Ï, such that t is syntactically equal to sÏ. Then t is
replaced by s'Ï. The simplifier tries to do this for all subterms of the
goal.
Recall, power_add is the theorem: ?a ^ (?m + ?n) = ?a ^ ?m * ?a ^ ?n
Now, for your proof attempts:
> lemma
> fixes a::real
> shows "a^6 = a^3 * a^3"
> using [[simp_trace=true]]
> using power_add [of a 3 3]
> by simp
This works as the simplifier can rewrite "3 + 3" to 6 and can then solve
the goal by rewriting with "a^6 = a^3 * a^3".
> using power_add
The simplifier cannot rewrite "?m + ?n" to anything. It also does not match the "6" in the goal.
> apply (simp add: power_add)
Similar. "a^6" does not match "?a ^ (?m + ?n)".
In my opinion, the nicest proof is:
apply (simp add: power_add[symmetric])
The [symmetric] reverses the equation.
-- Lars

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