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Proof step 402 from proof inv-write_inode (previous step)

afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), ino ∈ icache, m ∈ files ⊦ m ∈ icache, icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files ∧ icache[ino].inode.nlink = (icache[ino].inode.ino = m ⊃ (files[icache[ino].inode.ino].meta:= md).size:= m2;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, (icache[ino].inode.ino = m ⊃ (files[icache[ino].inode.ino].meta:= md).size:= m2;files[icache[ino].inode.ino]).meta, false, (icache[ino].inode.ino = m ⊃ (files[icache[ino].inode.ino].meta:= md).size:= m2;files[icache[ino].inode.ino]).nlink, 0, (icache[ino].inode.ino = m ⊃ (files[icache[ino].inode.ino].meta:= md).size:= m2;files[icache[ino].inode.ino]).size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 403:
icache[ino].inode = mkinode(m0, md0, boolvar, m1, m3, m4), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, ino ∈ icache ⊦ m ∈ icache, m0 = ino ∧ (icache[ino].dirty ⊃ m0 ∈ files ∧ m1 = (m0 = m ⊃ (files[m0].meta:= md).size:= m2;files[m0]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = m ⊃ (files[m0].meta:= md).size:= m2;files[m0]).meta, false, (m0 = m ⊃ (files[m0].meta:= md).size:= m2;files[m0]).nlink, 0, (m0 = m ⊃ (files[m0].meta:= md).size:= m2;files[m0]).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, m0, md0, boolvar, m1, m3, m4]

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, m0, md0, boolvar, m1, m3, m4