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Proof step 133 from proof fsync-inode-inv (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files ⊦ ∀ ino. ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))] → icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = ino ∧ (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].dirty ⊃ valid-file-inode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]) ; valid-ino(ino, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]) ∧ valid-inode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode, dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 134:
icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], m ∈ files, m ∈ icache, m1 ∈ files ⊦ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = ino ∧ (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].dirty ⊃ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino ∈ files ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.nlink = (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .nlink ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode = (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].meta, true, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].nlink, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].nsubdirs, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].size) ;mkinode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .meta, false, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .nlink, 0, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][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)