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Proof step 56 from proof inv-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, content[pageno])][datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar, inode), afs-cons(dirs, files), synced(files, icache, pcache), datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], m ∈ files, pageno ∈ content, ino ∈ files, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 57:
# buf0 = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), pcache[datakey(m, pageno), mkpentry(false, content[pageno])][datakey(ino, n)] = mkpentry(true, buf), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), synced(files, icache, pcache), ino ∈ files, pageno ∈ content, m ∈ files, datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])], ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ content[pageno] = zeropage, datakey(ino, n) = datakey(m, pageno), datakey(m, pageno) ∈ pcache

Rule argument

fma: datakey(ino, n) = datakey(m, pageno)

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws) Used formulas: datakey(ino, n) = datakey(m, pageno)