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Proof step 77 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], pcache)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 79:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), m ∈ dirs, m ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)] → synced(ino, icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], pcache)

Rule argument

spec: cache-base name: synced-dirs-variant1 seq: ⊦ synced(dirs, icache, pcache) → ( ¬ synced(dirs0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0))) subst: [dirs, icache, pcache, dirs0, icache0, pcache0] → [dirs, icache, pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache [m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5)) ], pcache] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], pcache