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Proof step 314 from proof refine-link (previous step)

cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m5, md1, # links(entries[str], cache_dirs), content), cache_dirs[m] = mkdir(m7, md5, # links(m, cache_dirs), m11, entries1), entries0[str] = entries[str], cache_files[entries[str]] = mkfile(m1, md4, # links(entries[str], cache_dirs), content0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), entries[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, ino ∈ cache_dirs, ino0 ∈ cache_dirs, str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ str0 ∈ entries1, ∃ ino1. ino1 ∈ cache_dirs ∧ (links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO) ∧ str ∈ cache_dirs[ino1].entries ∧ entries[str] = cache_dirs[ino1].entries[str]

User applied rule exists right

And closed the goal!

Rule argument

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

Additional information

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