Apologies to the original author of
TheoremProving, but, having proven a few theorems in my time, but I thought your claims were, basically, false, and it wasn't clear what you were trying to get at anyway...so I deleted them and left a little about what was correct and generally-accepted and -understood on the topic.
Please remove this comment when you see it. :-)
Can anything be said in generality besides theorem proving has a tendency to go:
- Theorem: Statement of thm.
- Proof: This, that,the other, Lemma1, Lemma2, special case, QED.
- follows from two previous statements by the rule of modus ponens
Typically, proofs of all sorts make use of various inference rules, not just modus ponens. Am I not understanding something? --
LMS
In the formal mathematical definition, only modus ponens is allowed, since it's all that's needed and things should be kept simple. Anything else is considered to be a shorthand for several intermediate steps. --JG