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Proof step 7 from proof afs-cons-inode-sync (previous step)

afs-cons(dirs, files), inode.ino ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ (ino = inode.ino ⊃ (files[inode.ino].size:= inode.size).meta:= inode.meta;files[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = inode.ino ⊃ (files[inode.ino].size:= inode.size).meta:= inode.meta;files[ino]).content → # (ino = inode.ino ⊃ (files[inode.ino].size:= inode.size).meta:= inode.meta;files[ino]).content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ (ino = m ⊃ (files[m].size:= m2).meta:= md;files[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ (files[m].size:= m2).meta:= md;files[ino]).content → # (ino = m ⊃ (files[m].size:= m2).meta:= md;files[ino]).content[n] = VFS_PAGE_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] → [inode, m, md, boolvar, m0, m1, m2]

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: inode, m, md, boolvar, m0, m1, m2