Repair the plainly modality
Change proposition extensionality into:
bi_plainly ((P -∗ Q) ∧ (Q -∗ P)) ⊢ P ≡ Q
This was suggested by @jjourdan, and @amintimany proved that this axiom holds in the ordered RA model. This MR shows that it also holds for monPred
. This should thus solve the paradox in #149 (closed).
If we accept this MR, I don't think there is a need for !98 (closed) anymore. It shows that we can define a plainly
modality on any logic we currently care about.
At the same time, this MR removes the following axiom for plainly
:
bi_plainly (bi_persistently P) ⊢ bi_plainly P
This axiom turned out to be admissible.
In terms of axioms, I very much like the current axioms. This way, plainly
behaves in the same way as persistently
and bi_valid
.