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Proof step 206 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ m ∈ 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, (icache[ino].inode.ino = m ⊃ mkdir(m0, md, # links(icache[ino].inode.ino, dirs), m2, entries);dirs[icache[ino].inode.ino]).meta, true, (icache[ino].inode.ino = m ⊃ mkdir(m0, md, # links(icache[ino].inode.ino, dirs), m2, entries);dirs[icache[ino].inode.ino]).nlink, (icache[ino].inode.ino = m ⊃ mkdir(m0, md, # links(icache[ino].inode.ino, dirs), m2, entries);dirs[icache[ino].inode.ino]).nsubdirs, (icache[ino].inode.ino = m ⊃ mkdir(m0, md, # links(icache[ino].inode.ino, dirs), m2, entries);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) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 207:
icache[ino].inode = mkinode(m1, md1, boolvar, 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), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, ino ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ m ∈ icache, 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, (m1 = m ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[m1]).meta, true, (m1 = m ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[m1]).nlink, (m1 = m ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[m1]).nsubdirs, (m1 = m ⊃ mkdir(m0, md, # links(m1, dirs), m2, entries);dirs[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, md1, 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, md1, boolvar, m3, m4, m5