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Proof step 23 from proof refine-fsync (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, cache_files[m].nlink, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, m1 = cache_files[m].nlink, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ [cache_fsync# (mkinode(m, md, false, cache_files[m].nlink, 0, m2), asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨afs_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m4, content), cache_files[m] = mkfile(m3, md1, m4, content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, m1 = m4, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ [cache_fsync#(mkinode(m, md, false, m4, 0, m2), asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨afs_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0))

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[m], m3, md1, m4, 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[m], m3, md1, m4, content0