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Proof step 24 from proof inv-write_inode (previous step)

err = ESUCCESS, inode0 = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs[m, dirs[m].meta:= md], files), afs-cons(dirs, 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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
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)))

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md0, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md0, m1, m2, entries