The plausibly modality
Much of this is based on https://gitlab.mpi-sws.org/FP/iris-coq/merge_requests/184#note_31510 by @amintimany, but made to work for non-affine BIs and changed in such a way that it follows the Iris naming conventions.
Some TODOs:
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Should the modality be affine or absorbing? -
Could we change the definition so that the following result holds even if P
is not absorbing:Lemma plain_plausibly P `{!Plain P, !Absorbing P} : <plausible> P ⊣⊢ P.
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The properties that the modality commutes with ▷
and∀
are pretty useless because they only hold when the proposition inside is plain (they thus trivially follow fromplain_plausibly
). Do we have such lemmas in general for some connectives? Otherwise, I propose to remove these lemmas. -
It would be useful to have some proof mode instances to support easy reasoning using the modality. @amintimany has some in his post, but what we had is not complete.
cc @jtassaro