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Proof step 14 from proof refine-renam (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]] = mkfile(m15, md3, m16, content), 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_dirs[m].entries[str], m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, new_child_inode = mkinode(m7, md1, boolvar, m8, m9, m10), new_dent = old_dent1, new_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), old_child_inode = mkinode(cache_dirs[m].entries[str], md2, boolvar0, m12, m13, m14), old_dent = mkdentry(str, cache_dirs[m].entries[str]), old_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].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), m ∈ cache_dirs, str ∈ cache_dirs[m].entries, m3 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m → md0 = md, (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.negdentry? ∨ (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (old_dent1.ino ∈ cache_dirs ∨ old_dent1.ino ∈ cache_files) ∧ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.ino = cache_dirs[m3].entries[old_dent1.name] ∧ old_dent1.dentry? ∧ ( old_dent1.ino ∈ cache_dirs ∧ m8 = cache_dirs[old_dent1.ino].nlink ∧ m10 = cache_dirs[old_dent1.ino].size ∧ m9 = cache_dirs[old_dent1.ino].nsubdirs ∧ boolvar ∨ old_dent1.ino ∈ cache_files ∧ m8 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[old_dent1.ino].nlink ∧ m9 = 0 ∧ ¬ boolvar) ∧ m7 = old_dent1.ino ∧ (old_dent1.ino ∈ cache_files ↔ cache_dirs[m].entries[str] ∈ cache_files) ∧ (old_dent1.ino ∈ cache_dirs → old_dent1.ino ≠ ROOT_INO ∧ cache_dirs[old_dent1.ino].entries = ∅), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, cache_dirs[m].entries[str] ∈ cache_dirs ∨ cache_dirs[m].entries[str] ∈ cache_files, cache_dirs[m].entries[str] ∈ cache_dirs ∧ m12 = cache_dirs[cache_dirs[m].entries[str]].nlink ∧ m14 = cache_dirs[cache_dirs[m].entries[str]].size ∧ m13 = cache_dirs[cache_dirs[m].entries[str]].nsubdirs ∧ boolvar0 ∨ cache_dirs[m].entries[str] ∈ cache_files ∧ m12 = m16 ∧ m13 = 0 ∧ ¬ boolvar0 ⊦ ⟪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)⟫ ⟨old_dent0 := mkdentry(str, m11); p_inode := mkinode(m, md, true, m0, m1, m2); p_inode0 := mkinode(m3, md0, true, m4, m5, m6); p_inode2 := mkinode(m7, md1, boolvar, m8, m9, m10); p_inode1 := mkinode(m11, md2, boolvar0, m12, m13, m14); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]] = mkfile(m15, md3, m16, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[old_dent1.ino] = mkfile(m17, md4, m18, content0), 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_dirs[m].entries[str], m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, new_child_inode = mkinode(m7, md1, boolvar, m8, m9, m10), new_dent = old_dent1, new_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), old_child_inode = mkinode(cache_dirs[m].entries[str], md2, boolvar0, m12, m13, m14), old_dent = mkdentry(str, cache_dirs[m].entries[str]), old_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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), m3 ∈ cache_dirs, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, m3 = m → md0 = md, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_dirs[m].entries[str] ∈ cache_dirs ∧ m12 = cache_dirs[cache_dirs[m].entries[str]].nlink ∧ m14 = cache_dirs[cache_dirs[m].entries[str]].size ∧ m13 = cache_dirs[cache_dirs[m].entries[str]].nsubdirs ∧ boolvar0 ∨ cache_dirs[m].entries[str] ∈ cache_files ∧ m12 = m16 ∧ m13 = 0 ∧ ¬ boolvar0, cache_dirs[m].entries[str] ∈ cache_dirs ∨ cache_dirs[m].entries[str] ∈ cache_files, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.negdentry? ∨ (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (old_dent1.ino ∈ cache_dirs ∨ old_dent1.ino ∈ cache_files) ∧ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.ino = cache_dirs[m3].entries[old_dent1.name] ∧ old_dent1.dentry? ∧ ( old_dent1.ino ∈ cache_dirs ∧ m8 = cache_dirs[old_dent1.ino].nlink ∧ m10 = cache_dirs[old_dent1.ino].size ∧ m9 = cache_dirs[old_dent1.ino].nsubdirs ∧ boolvar ∨ old_dent1.ino ∈ cache_files ∧ m8 = m18 ∧ m9 = 0 ∧ ¬ boolvar) ∧ m7 = old_dent1.ino ∧ (old_dent1.ino ∈ cache_files ↔ cache_dirs[m].entries[str] ∈ cache_files) ∧ (old_dent1.ino ∈ cache_dirs → old_dent1.ino ≠ ROOT_INO ∧ cache_dirs[old_dent1.ino].entries = ∅) ⊦ ⟪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)⟫ ⟨old_dent0 := mkdentry(str, m11); p_inode := mkinode(m, md, true, m0, m1, m2); p_inode0 := mkinode(m3, md0, true, m4, m5, m6); p_inode2 := mkinode(m7, md1, boolvar, m8, m9, m10); p_inode1 := mkinode(m11, md2, boolvar0, m12, m13, m14); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ 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 ⊕ cache_pcache) ⊕ cache_icache)[old_dent1.ino], m17, md4, m18, 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 ⊕ cache_pcache) ⊕ cache_icache)[old_dent1.ino], m17, md4, m18, content0