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Proof step 172 from proof afs-cons-rename-file-negdentry (previous step)

dirs0[m0] = mkdir(m1, md4, # links(m0, dirs0), m5, entries0), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(0, md2, # links(m, dirs0), m4, entries1), m0 ∈ dirs0, entries1[str] ∈ files, m ∈ dirs0, str ∈ entries1, ROOT_INO ∈ dirs0, m0 = m → md1 = md0, ∀ ino. (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files → ¬ ino ∈ dirs0 ∧ files[ino].nlink = # links(ino, dirs0)) ∧ (∀ name. ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries0

User applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: m abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ # entries = 0 ↔ entries = ∅; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ ¬ str ∈ ∅; (s) Used terms: m