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Proof step 7 from proof inv-fsync (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced → synced(files, icache, pcache) ⊦ ⟪cache_fsync#(mkinode(m, md, false, # links(m, dirs), 0, m2), asynced0, asynced; dirs, files, icache, pcache, asynced1; err)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

User applied rule call right

And obtained the following new goals

Proof step 8:
asynced1 ↔ asynced4, asynced0 ↔ asynced2, asynced ↔ asynced3, files[m] = mkfile(m0, md0, # links(m, dirs), content), inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced2 → synced(files, icache, pcache) ⊦ ⟪if valid-file-inode(inode, dirs, files) then {err := ESUCCESS; if ¬ asynced0 then {cache_fsync-pages#(inode, dirs; err, files, pcache, asynced); if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)}} else abort⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

pos: right 1

Additional information

Used simplifier rules: fsync: ⊦ ;