No one would argue against the idea/ observation that proofs are very important in mathematics. Some people are trying to make their notations on a blackboard during a lecture as consistent as possible with their course notes or textbooks; including full reproduction of rigorous and detailed proofs for all theorems, corollaries and so on. On the other hand, some believe that the theory with detailed proofs should be in textbooks, while it is crucially important to explain main ideas via examples. So, my question is:
How do you think, what is more important at a lecture: 1) to give a rigorous proof or 2) only formulate a statement and give an intuitive understanding via illustrative examples?
P.S.: I understand that it would be great to do both. But in real life we have natural time limitations. And feel free to edit this post because of my bad English :).
Edit: this is for undergraduate and graduate level.