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Proof step 23 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, m1, content), err = ESUCCESS, afs-cons(dirs, files[m, files[m].content:= content[pageno, buf]]), afs-cons(dirs, files), 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 ⊦ ⟪asynced2 := false; if err = ESUCCESS then pcache_set#(m, pageno, buf, asynced2; err, pcache)⟫ ( icache-cons(icache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ dcache-cons(dcache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ pcache-cons(pcache, dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ synced(dirs, icache, pcache) ∧ synced(files[m, files[m].content:= content[pageno, buf]], icache, pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# 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 ⊦ ⟪asynced2 := false; if err = ESUCCESS then pcache_set#(m, pageno, buf, asynced2; 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (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