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Proof step 456 from proof inv-rename-file-dentry (previous step)

pcache[datakey(ino, n)] = mkpentry(boolvar, buf), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), icache0[ino] = mkientry(boolvar0, inode), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, ino ∈ dirs0, asynced2 → synced(files, icache0, pcache), ino ∈ icache0 → ¬ boolvar0, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ( ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] → ¬ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] .dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 457:
icache0[ino] = mkientry(boolvar0, inode), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] = mkientry(boolvar1, inode0), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), ino ∈ dirs0, entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, ino ∈ icache0 → ¬ boolvar0, asynced2 → synced(files, icache0, pcache), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ( ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0 [m3, mkientry (false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ], boolvar1, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0 [m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ], boolvar1, inode0