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Proof step 36 from proof write-inode-inv (previous step)

files1 -- ino = files0 -- ino, (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);mkfile(m1, md0, m2, content1)) = mkfile(m3, md1, m4, content2), dirs[ino0] = mkdir(m5, md2, m6, m7, entries), files0[ino] = mkfile(m, md, m0, content0), files1[ino] = mkfile(m, md, # links(ino, dirs), content), files1[ino0] = mkfile(m1, md0, m2, content1), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ino ∈ files0, ino ∈ files1, ROOT_INO ∈ dirs, n ≤ # buf, n1 ≤ # buf, n ≤ n1, ino0 ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files1, ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries = ∅, ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ m2 = # links(ino0, dirs), ino0 ∈ dirs → m6 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m5 = # entries ∧ m7 = # subdirs(ino0, dirs) ⊦ (ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ m4 = # links(ino0, dirs)) ∧ (ino0 ∈ files1 ∧ n0 ∈ content2 → # content2[n0] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = ino0

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base Used formulas: ino = ino0