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Proof step 51 from proof afs-cons-rename-file-negdentry (previous step)

# links(m0, dirs0) = dirs0[m0].nlink, dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str)] [m0, ( (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);dirs0[m0]) .entries:= (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);dirs0[m0]).entries[str0, entries1[str]]) .size:= ((m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);dirs0[m0]).size + 1) ], afs-cons(dirs0, files), m0 ∈ dirs0, entries1[str] ∈ files, m ∈ dirs0, str ∈ entries1, ¬ str0 ∈ entries, ¬ entries1[str] ∈ dirs0, ¬ str0 ∈ dirs0[m0].entries, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m5, m2 + 1); dirs, files); afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), dirs0[m0].nsubdirs, dirs0[m0].size); dirs, files); skip; old_parent_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) ); new_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
# links(m0, dirs0) = dirs0[m0].nlink, (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);dirs0[m0]) = mkdir(m1, md4, m4, m6, entries0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str)] [m0, ((m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);dirs0[m0]).entries:= entries0[str0, entries1[str]]).size:= (m1 + 1) ], afs-cons(dirs0, files), str ∈ entries1, m ∈ dirs0, entries1[str] ∈ files, m0 ∈ dirs0, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m5, m2 + 1); dirs, files); afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), dirs0[m0].nsubdirs, dirs0[m0].size); dirs, files); skip; old_parent_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) ); new_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries, entries1[str] ∈ dirs0, str0 ∈ dirs0[m0].entries

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [(m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str) ;dirs0[m0] ), m1, md4, m4, m6, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str) ;dirs0[m0] ), m1, md4, m4, m6, entries0