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Proof step 6 from proof afs-cons-non0 (previous step)

entries[str] = 0, dirs[ino] = mkdir(n0, md, # links(ino, dirs), n1, entries), ino ∈ dirs, str ∈ entries, ROOT_INO ∈ dirs, ∀ ino0. (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅) ∧ ( ino0 ∈ dirs → ¬ ino0 ∈ files ∧ dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs)) ∧ (ino0 ∈ files → ¬ ino0 ∈ dirs ∧ files[ino0].nlink = # links(ino0, dirs)) ∧ (∀ name. ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files) ∧ (∀ n. ino0 ∈ files ∧ n ∈ files[ino0].content → # files[ino0].content[n] = VFS_PAGE_SIZE) ⊦

User applied rule all left

And obtained the following new goals

Proof step 7:
dirs[ino] = mkdir(n0, md, # links(ino, dirs), n1, entries), entries[str] = 0, ROOT_INO ∈ dirs, str ∈ entries, ino ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → ¬ ino ∈ files ∧ 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), ∀ ino0. (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅) ∧ ( ino0 ∈ dirs → ¬ ino0 ∈ files ∧ dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs)) ∧ (ino0 ∈ files → ¬ ino0 ∈ dirs ∧ files[ino0].nlink = # links(ino0, dirs)) ∧ (∀ name. ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files) ∧ (∀ n. ino0 ∈ files ∧ n ∈ files[ino0].content → # files[ino0].content[n] = VFS_PAGE_SIZE), ∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE ⊦

Rule argument

pos: left 6 terms: ino abort: F discard: F computed: T

Additional information

Used terms: ino