AW: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Discher, Samiro
According to https://math.stackexchange.com/questions/1123312/theory-of-definitions, (referencing the same book as the question you mentioned) these properties are required by all definitions, and there are also some criteria listed and explained for a certain type of definition. Maybe this is a

Re: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Marshall Stoner
Thanks. I got it. I'm rusty with LaTex and forgot about redefinition commands. It was late when I looked so I gave up when I got errors. It is what I thought it was. I have proved line 8 of 4.2 in a different way from other results. I wrote it as... ⊢ eq( φ ,φ ) where I define eq( phi ,

AW: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Discher, Samiro
"I couldn't convert them to something I could actually read like latex or unicode" The proof format is meant to allow readability by both machines (easy and flexible when able to code) and humans (in a text editor without word wrapping). Apart from some missing spaces, these formulas are in

Re: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Mario Carneiro
The justification of definitions requires imposing additional structure on metamath databases in the form of being able to unambiguously parse statements into trees. Without it, you can't use the definition checker at all, and the rules do not make sense / could be circumvented without more rules.

Re: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Marshall Stoner
Sorry I didn't have time to read the proof you shared. I couldn't read it easily and wasn't sure if it completely answered what I really wanted since I want to show that definitions satisfy the precise meaning of eliminability and non-creativity. Maybe the proofs help but I couldn't convert

Re: [Metamath] Uncomfortable with definitions as axioms ... help?

2023-07-12 Thread Marshall Stoner
I wasn't talking about set.mm or mmj2. I was talking in metamath in general, which doesn't seem to enforce non-ambiguity since it only reads strings of tokens with no other underlying structure. I was in learning the definition checker rules in terms of learning in detail how definitions are