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Proof step 90 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) = mkfile(m4, md1, m5, content1), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files1[ino] = mkfile(m2, md0, m3, content), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons (of, dirs, files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)]), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1, 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 ∈ files1 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs) ⊦ n0 = 0, n2 = 0, (ino ∈ files1 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files1 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 91:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) = mkfile(m4, md1, m5, content1), files1[ino] = mkfile(m2, md0, m3, content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs[ino] = mkdir(m6, md2, m7, m8, entries), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)]), ROOT_INO ∈ dirs, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino ∈ files1 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs → m7 = # links(ino, dirs) ∧ m7 ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files1 ⊦ n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, (ino ∈ files1 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files1 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino], m6, md2, m7, m8, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino], m6, md2, m7, m8, entries