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Proof step 79 from proof inv-write_inode (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
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, ino ∈ dirs, asynced2 → synced(files, icache, pcache), ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ( ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))] → ¬ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)

Rule argument

Additional information

Used simplifier rules: ⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)