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Proof step 117 from proof inv-evict (previous step)

# links(m, dirs) = 0, icache[ino].inode = mkinode(m1, md0, boolvar, m3, m4, m5), dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ino = m, m = ROOT_INO, m1 = ino ∧ (icache[ino].dirty ⊃ ino ∈ files ∧ m3 = files[ino].nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m3, m4, m5) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 118:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), icache[ino] = mkientry(boolvar0, inode), inode = mkinode(m1, md0, boolvar, m3, m4, m5), afs-cons(dirs, files), afs-cons(dirs -- m, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, ino ∈ icache, asynced1 → synced(files, icache, pcache) ⊦ ino = m, m = ROOT_INO, m1 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m3 = files[ino].nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m3, m4, m5) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar0, inode