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Proof step 115 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs, files), afs-cons(dirs -- m, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, ino ∈ icache, asynced1 → synced(files, icache, pcache) ⊦ ino = m, m = ROOT_INO, 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 -- m)[icache[ino].inode.ino].meta, true, (dirs -- m)[icache[ino].inode.ino].nlink, (dirs -- m)[icache[ino].inode.ino].nsubdirs, (dirs -- m)[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) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 116:
# links(m, dirs) = 0, icache[ino].inode = mkinode(m1, md0, boolvar, m3, m4, m5), dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ino = m, m = ROOT_INO, m1 = ino ∧ (icache[ino].dirty ⊃ m1 ∈ files ∧ m3 = files[m1].nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (m1 ∈ dirs ⊃ mkinode(m1, (dirs -- m)[m1].meta, true, (dirs -- m)[m1].nlink, (dirs -- m)[m1].nsubdirs, (dirs -- m)[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ) )

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache[ino].inode, m1, md0, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[ino].inode, m1, md0, boolvar, m3, m4, m5