Could you explain that? Here’s my guess at what you mean: “If ⊢B and the shortest proof of B in classical logic contains the statement A, or if A⊢B but not ⊢B, then A → B in ‘compressed logic’.”
It’s really just simplifying the logical expression. Like (A and not A) = True. I think that’s what you’re getting at, although I’m not familiar with your notation, and don’t want to think too hard.
Could you explain that? Here’s my guess at what you mean: “If ⊢B and the shortest proof of B in classical logic contains the statement A, or if A⊢B but not ⊢B, then A → B in ‘compressed logic’.”
It’s really just simplifying the logical expression. Like (A and not A) = True. I think that’s what you’re getting at, although I’m not familiar with your notation, and don’t want to think too hard.