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Proof step 25 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, m1, m2, entries), err = ESUCCESS, inode0 = mkinode(m, md, true, m1, m2, m0), afs-cons(dirs, files), afs-cons(dirs[m, dirs[m].meta:= md], files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ ⟪asynced3 := false; if err = ESUCCESS then icache_get#(inode0.ino, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := inode0.meta; if ¬ inode0.directory then inode1.size := inode0.size; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons(icache, dirs[m, dirs[m].meta:= md], files) ∧ dcache-cons(dcache, dirs[m, dirs[m].meta:= md], files) ∧ pcache-cons(pcache, dirs[m, dirs[m].meta:= md], files) ∧ synced(dirs[m, dirs[m].meta:= md], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), err = ESUCCESS, inode0 = mkinode(m, md, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ ⟪asynced3 := false; if err = ESUCCESS then icache_get#(inode0.ino, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := inode0.meta; if ¬ inode0.directory then inode1.size := inode0.size; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons(icache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ dcache-cons(dcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ pcache-cons(pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base