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Proof step 12 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), m ∈ 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 = m ⊃ files[m].content:= files[m].content[pageno, buf];files[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ files[m].content:= files[m].content[pageno, buf];files[ino]).content → # (ino = m ⊃ files[m].content:= files[m].content[pageno, buf];files[ino]).content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# buf = VFS_PAGE_SIZE, files[ino] = mkfile(m0, md, m1, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ files ∧ n ∈ content → # 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 ∧ m1 = # 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].content:= files[m].content[pageno, buf];files[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ files[m].content:= files[m].content[pageno, buf];files[ino]).content → # (ino = m ⊃ files[m].content:= files[m].content[pageno, buf];files[ino]).content[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[ino], m0, md, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[ino], m0, md, m1, content