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Proof step 29 from proof inv-link (previous step)

dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries0[str] = entries[str], files[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs), content0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries[str] ∈ files, asynced → synced(files, icache, pcache), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries1, ∃ ino1. ino1 ∈ dirs ∧ (links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO) ∧ str ∈ dirs[ino1].entries ∧ entries[str] = dirs[ino1].entries[str]

Heuristic use patterns applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: ino0 abort: T discard: F computed: F

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used terms: ino0