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Proof step 39 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), err = ESUCCESS, afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], 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 ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ ⟪icache_set#(icache[m].inode.meta:= md, false; err, icache)⟫ ( 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)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, inode), err = ESUCCESS, 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, m ∈ icache, asynced2 → synced(files, icache, pcache) ⊦ ⟪icache_set#(inode.meta:= md, false; err, icache)⟫ ( 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

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[m], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode