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Proof step 317 from proof refine-link (previous step)

cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), 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), entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ str0 ∈ entries, (∃ ino0. ino0 ∈ cache_dirs ∧ (links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO) ∧ str ∈ cache_dirs[ino0].entries ∧ entries0[str] = cache_dirs[ino0].entries[str]) ∧ m7 = cache_files[entries0[str]].nlink

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 318:
cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), cache_files[entries0[str]] = mkfile(m1, md, m3, content0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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), ino ∈ cache_dirs, str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries, (∃ ino0. ino0 ∈ cache_dirs ∧ (links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO) ∧ str ∈ cache_dirs[ino0].entries ∧ entries0[str] = cache_dirs[ino0].entries[str]) ∧ m7 = m3

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [cache_files[entries0[str]], m1, md, m3, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: cache_files[entries0[str]], m1, md, m3, content0