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Proof step 247 from proof inv-link (previous step)

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

Heuristic use patterns applied rule exists right

And closed the goal!

Rule argument

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

Additional information

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