[STATEMENT]
lemma pi_gt3: "pi > 3"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. 3 < pi
[PROOF STEP]
using pi_approx
[PROOF STATE]
proof (prove)
using this:
3141592653588 / 10 ^ 12 \<le> pi
pi \<le> 31415926535899 / 10 ^ 13

goal (1 subgoal):
 1. 3 < pi
[PROOF STEP]
by simp