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Proof step 81 from proof inv-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key] = mkpentry(boolvar, buf), files[m] = mkfile(m0, md, # links(m, dirs), content), files[key.ino] = mkfile(m1, md0, m2, content0), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], m ∈ files, pageno ∈ content, asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 82:
# buf0 = VFS_PAGE_SIZE, files[key.ino] = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key] = mkpentry(boolvar, buf), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), pageno ∈ content, m ∈ files, key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, key = datakey(m, pageno), datakey(m, pageno) ∈ pcache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

Rule argument

fma: key = datakey(m, pageno)

Additional information

Used simplifier rules: ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: key = datakey(m, pageno)