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Proof step 111 from proof fsync-inode-inv (previous step)

# files[key.ino].content[key.part] = VFS_PAGE_SIZE, (key.ino = m1 ⊃ mkfile(m4, md, # links(key.ino, dirs), content0);files[key.ino]) = mkfile(m2, md3, m3, content1), pcache[key] = mkpentry(false, files[key.ino].content[key.part]), 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), key.data?, afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), synced(dirs, icache, pcache), key.part ∈ files[key.ino].content, key ∈ pcache, m ∈ files, m ∈ icache, m1 ∈ files, key.ino ∈ files, ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ key.part ∈ content1 ∧ files[key.ino].content[key.part] = content1[key.part]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 112:
# files[m6].content[m10] = VFS_PAGE_SIZE, (m6 = m1 ⊃ mkfile(m4, md, # links(m6, dirs), content0);files[m6]) = mkfile(m2, md3, m3, content1), 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(false, files[m6].content[m10]), key = datakey(m6, m10), key.data?, afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), synced(dirs, icache, pcache), m6 ∈ files, m1 ∈ files, m ∈ icache, m ∈ files, key ∈ pcache, m10 ∈ files[m6].content, ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ m10 ∈ content1 ∧ files[m6].content[m10] = content1[m10]

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key, m6, m10]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m6, m10