Prove different versions of Löb rule
- May 25, 2020
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Robbert Krebbers authored016cd820
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Robbert Krebbers authored7253dafb
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This MR follows a discussion with @dreyer @amintimany and @birkedal about a version of Löb without implication. We came up with □ (▷ P -∗ P) ⊢ P
and showed it's equivalent to the normal Löb rule in affine BIs (lemma löb_alt
in this MR).
I then spend an hour staring and trying to generalize löb_alt
to non-affine BIs, but gave up.
This MR adds the following lemmas:
Lemma löb_wand_intuitionistically `{!BiLöb PROP} P : □ (□ ▷ P -∗ P) ⊢ P.
Lemma löb_wand `{!BiLöb PROP} P : □ (▷ P -∗ P) ⊢ P.
Lemma löb_alt `{!BiAffine PROP} : BiLöb PROP ↔ ∀ P, □ (▷ P -∗ P) ⊢ P.
Also, it shortens the proof of tac_löb
via löb_wand_intuitionistically
.