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Proof step 42 from proof inv-write_inode (previous step)

asynced ↔ false, dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, inode0), err = ESUCCESS, inode = inode0.meta:= md, afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, m ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ icache-cons(icache[inode.ino, mkientry(asynced, inode)], dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ dcache-cons(dcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ pcache-cons(pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache[inode.ino, mkientry(asynced, inode)], pcache) ∧ (asynced2 → synced(files, icache[inode.ino, mkientry(asynced, inode)], pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
icache[m] = mkientry(boolvar, inode0), 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), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ icache-cons(icache[inode0.ino, mkientry(false, inode0.meta:= md)], dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ dcache-cons(dcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ pcache-cons(pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache[inode0.ino, mkientry(false, inode0.meta:= md)], pcache) ∧ (asynced2 → synced(files, icache[inode0.ino, mkientry(false, inode0.meta:= md)], pcache))

Rule argument

Additional information

Used simplifier rules: ⊦ (inode.meta:= md).ino = inode.ino; (s)