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Proof step 26 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), err = ESUCCESS, afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ ⟪pcache_set#(m, pageno, buf, false; err, pcache)⟫ ( icache-cons(icache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ dcache-cons(dcache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ pcache-cons(pcache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])], icache, pcache))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 27:
# buf = VFS_PAGE_SIZE, asynced ↔ false, files[m] = mkfile(m0, md, # links(m, dirs), content), err = ESUCCESS, ino = m, afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪let key = datakey(ino, pageno), pe = mkpentry(asynced, buf) in pcache[key] := pe⟫ ( icache-cons(icache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ dcache-cons(dcache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ pcache-cons(pcache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])], icache, pcache))

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_set#(INO, PAGENO, BUF, DIRTY; ERR, PCACHE) {let KEY = datakey(INO, PAGENO), PE = mkpentry(DIRTY, BUF) in PCACHE[KEY] := PE };