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The plausibly modality

Robbert Krebbers requested to merge robbert/plausibly into master

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:

  • 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.
  • 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 from plain_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

Edited by Amin Timany

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