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Proof step 401 from proof inv-write_inode (previous step)

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 ⊦ m ∈ icache, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files[m, (files[m].meta:= md).size:= m2]) ; valid-ino(ino, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ valid-inode(icache[ino].inode, dirs, files[m, (files[m].meta:= md).size:= m2]) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 402:
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) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)