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Proof step 15 from proof refine-rename-file-dentry (previous step)

afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m11 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m3].entries[str0]].nlink, m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m7 = cache_dirs[m].entries[str], m8 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]].nlink, m9 = cache_dirs[m3].entries[str0], new_child_inode = mkinode(cache_dirs[m].entries[str], md1, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]].nlink, 0, m10), new_dent = mkdentry(str, cache_dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), old_child_inode = mkinode(cache_dirs[m3].entries[str0], md2, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m3].entries[str0]].nlink, 0, m13), old_dent = mkdentry(str0, cache_dirs[m3].entries[str0]), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), 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), str ∈ cache_dirs[m].entries, str0 ∈ cache_dirs[m3].entries, m ∈ cache_dirs, m3 ∈ cache_dirs, cache_dirs[m].entries[str] ∈ cache_files, cache_dirs[m3].entries[str0] ∈ cache_files, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, m7); old_dent0 := mkdentry(str0, m9); new_parent_inode0 := mkinode(m, md, true, m0, m1, m2); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); new_child_inode0 := mkinode(m7, md1, false, m8, 0, m10); old_child_inode0 := mkinode(m9, md2, false, m11, 0, m13); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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 ⊕ cache_pcache) ⊕ cache_icache )[cache_dirs[m].entries[str] ], m12, md3, m14, content]

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 ⊕ cache_pcache) ⊕ cache_icache )[cache_dirs[m].entries[str] ], m12, md3, m14, content