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Proof step 406 from proof inv-write_inode (previous step)

icache[ino] = mkientry(boolvar0, mkinode(m0, md0, boolvar, m1, m3, m4)), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, ino ∈ icache ⊦ m ∈ icache, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m3, m4) = (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 use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 407:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 408:
icache[ino] = mkientry(boolvar0, mkinode(m0, md0, boolvar, m1, m3, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), synced(dirs, icache, pcache), ino ∈ icache, m ∈ files, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files);valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files)) ⊦ m ∈ icache, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m3, m4) = (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: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [icache, dirs, files] → [icache, dirs, files] flags: <all paths>

Additional information

Used terms: icache, dirs, files