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Proof step 29 from proof inv-create (previous step)

# links(m, dirs0) = dirs0[m].nlink, dirs0[m].entries:= dirs0[m].entries[str, ino] = mkdir(m0, md2, m1, m2, entries0), dirs0[m] = mkdir(dirs0[m].size, md1, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs = dirs0[m, mkdir(m0 + 1, md2, m1, m2, entries0)], files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], ino ≠ 0, afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ str ∈ dirs0[m].entries, ¬ str ∈ entries, ¬ ino ∈ files0, ¬ ino ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); 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, ino).ino, dirs, files); asynced := ?] ( afs-cons(dirs, files) → ⟪let asynced = false in {err := ESUCCESS; icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, str, mkdentry(str, ino); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
# links(m, dirs0) = m4, dirs0[m].entries:= entries1[str, ino] = mkdir(m0, md2, m1, m2, entries0), dirs0[m] = mkdir(m3, md1, m4, m5, entries), dirs0[m] = mkdir(m3, md3, m4, m5, entries1), dirs = dirs0[m, mkdir(m0 + 1, md2, m1, m2, entries0)], files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, m4, m5, 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, ino).ino, dirs, files); asynced := ?] ( afs-cons(dirs, files) → ⟪let asynced = false in {err := ESUCCESS; icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, str, mkdentry(str, ino); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), ino = 0, str ∈ entries1, str ∈ entries, ino ∈ files0, ino ∈ dirs0

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] → [dirs0[m], m3, md3, m4, m5, entries1]

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: dirs0[m], m3, md3, m4, m5, entries1