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Proof step 107 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), key ∈ dcache, m ∈ dirs, m ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ (key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries);dirs[key.ino]).entries ∧ dcache[key].ino = (key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries);dirs[key.ino]).entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 108:
(key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries);dirs[key.ino]) = mkdir(m6, md2, m7, m8, entries0), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, key ∈ dcache, asynced2 → synced(files, icache, pcache) ⊦ key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].dentry?

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] → [(key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries) ;dirs[key.ino] ), m6, md2, m7, m8, 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: (key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries) ;dirs[key.ino] ), m6, md2, m7, m8, entries0