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Proof step 25 from proof inv-link (previous step)

# links(entries0[str], dirs0) = files[entries0[str]].nlink, # links(m, dirs0) = dirs0[m].nlink, entries0[str] = dirs0[ino].entries[str], dirs0[m] = mkdir(dirs0[m].size, md2, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries0[str]] = mkfile(m0, md1, files[entries0[str]].nlink, content), dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), dirs = dirs0[m, (dirs0[m].entries:= dirs0[m].entries[str0, entries0[str]]).size:= (dirs0[m].size + 1)], afs-cons(dirs0, files), str ∈ dirs0[ino].entries, ino ∈ dirs0, ino0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries0[str] ∈ files, ¬ str0 ∈ dirs0[m].entries, ¬ str0 ∈ entries, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
# links(m, dirs0) = dirs0[m].nlink, # links(entries0[str], dirs0) = m4, dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), files[entries0[str]] = mkfile(m0, md1, m4, content), dirs0[m] = mkdir(dirs0[m].size, md2, dirs0[m].nlink, dirs0[m].nsubdirs, entries), entries0[str] = dirs0[ino].entries[str], files[entries0[str]] = mkfile(m1, md4, m4, content0), dirs = dirs0[m, (dirs0[m].entries:= dirs0[m].entries[str0, entries0[str]]).size:= (dirs0[m].size + 1)], afs-cons(dirs0, files), entries0[str] ∈ files, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino ∈ dirs0, str ∈ dirs0[ino].entries, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ dirs0[m].entries, str0 ∈ entries

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] → [files[entries0[str]], m1, md4, 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: files[entries0[str]], m1, md4, m4, content0