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Proof step 104 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache, m ∈ files, m ∈ icache, m1 ∈ files ⊦ key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = m1 ⊃ mkfile(m4, md, # links(key.ino, dirs), content0);files[key.ino]).content ∧ pcache[key].page = (key.ino = m1 ⊃ mkfile(m4, md, # links(key.ino, dirs), content0);files[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 105:
files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files, key ∈ pcache ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ boolvar → key.part ∈ (key.ino = m1 ⊃ mkfile(m4, md, # links(key.ino, dirs), content0);files[key.ino]).content ∧ buf = (key.ino = m1 ⊃ mkfile(m4, md, # links(key.ino, dirs), content0);files[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar, buf