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Proof step 113 from proof fsync-inode-inv (previous step)

# files[m6].content[m10] = VFS_PAGE_SIZE, (m6 = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[m6]) = mkfile(m2, md3, m3, content1), pcache[datakey(m6, m10)] = mkpentry(false, files[m6].content[m10]), 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), synced(dirs, icache, pcache), m10 ∈ files[m6].content, datakey(m6, m10) ∈ pcache, m ∈ files, m ∈ icache, m1 ∈ files, m6 ∈ 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]) ⊦ m10 ∈ content1 ∧ files[m6].content[m10] = content1[m10]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 114:
# content2[m10] = VFS_PAGE_SIZE, (m6 = m1 ⊃ mkfile(m4, md, # links(m1, 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[datakey(m6, m10)] = mkpentry(false, content2[m10]), files[m6] = mkfile(m11, md4, m12, content2), 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, datakey(m6, m10) ∈ pcache, m10 ∈ content2, ∀ 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 ∧ content2[m10] = content1[m10]

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m6], m11, md4, m12, content2]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m6], m11, md4, m12, content2