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Proof step 117 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), ino ∈ icache, m ∈ files ⊦ icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files ∧ icache[ino].inode.nlink = (icache[ino].inode.ino = m ⊃ mkfile(m0, md, # links(icache[ino].inode.ino, dirs), content[pageno, buf]);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 ⊃ mkfile(m0, md, # links(icache[ino].inode.ino, dirs), content[pageno, buf]);files[icache[ino].inode.ino]) .meta, false, (icache[ino].inode.ino = m ⊃ mkfile(m0, md, # links(icache[ino].inode.ino, dirs), content[pageno, buf]);files[icache[ino].inode.ino]) .nlink, 0, (icache[ino].inode.ino = m ⊃ mkfile(m0, md, # links(icache[ino].inode.ino, dirs), content[pageno, buf]);files[icache[ino].inode.ino]) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 118:
# buf = VFS_PAGE_SIZE, icache[ino].inode = mkinode(m1, md0, boolvar, m2, m3, m4), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files, ino ∈ icache ⊦ m1 = ino ∧ (icache[ino].dirty ⊃ m1 ∈ files ∧ m2 = (m1 = m ⊃ mkfile(m0, md, # links(m1, dirs), content[pageno, buf]);files[m1]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode (m1, (m1 = m ⊃ mkfile(m0, md, # links(m1, dirs), content[pageno, buf]);files[m1]).meta, false, (m1 = m ⊃ mkfile(m0, md, # links(m1, dirs), content[pageno, buf]);files[m1]).nlink, 0, (m1 = m ⊃ mkfile(m0, md, # links(m1, dirs), content[pageno, buf]);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, m2, 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, m1, md0, boolvar, m2, m3, m4