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Proof step 238 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), icache[ino] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m2, m3, m4)), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, ino ∈ icache, asynced1 → synced(files, icache, pcache), ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files ∧ icache[ino].inode.nlink = files[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, files[icache[ino].inode.ino].meta, false, files[icache[ino].inode.ino].nlink, 0, files[icache[ino].inode.ino].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ ino = m, m = ROOT_INO, m ∈ dirs, m1 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m2 = files[ino].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m2, m3, m4) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, (files -- m)[ino].meta, false, (files -- m)[ino].nlink, 0, (files -- m)[ino].size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 239:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), icache[m1] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m2, m3, m4)), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, m1 ∈ icache, asynced1 → synced(files, icache, pcache), (boolvar0 ⊃ m1 ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (m1 ∈ dirs ∨ m1 ∈ files) ∧ mkinode(m1, md0, boolvar, m2, m3, m4) = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, m1 = m, m ∈ dirs, (boolvar0 ⊃ m1 ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (m1 ∈ dirs ∨ m1 ∈ files) ∧ mkinode(m1, md0, boolvar, m2, m3, m4) = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, (files -- m)[m1].meta, false, (files -- m)[m1].nlink, 0, (files -- m)[m1].size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)