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Proof step 56 from proof fsync-inode-inv (previous step)

dirs[m1] = mkdir(m7, md2, # links(m1, dirs), m9, entries), icache[m] = mkientry(true, mkinode(m1, md, true, # links(m1, dirs), m9, m7)), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, m6, content0), afs-cons(dirs[m1, mkdir(m7, md, # links(m1, dirs), m9, 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 ∈ files, m1 ∈ dirs ⊦

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ 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 58:
files[m1] = mkfile(m5, md1, m6, content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(true, mkinode(m1, md, true, # links(m1, dirs), m9, m7)), dirs[m1] = mkdir(m7, md2, # links(m1, dirs), m9, entries), afs-cons(dirs, files), afs-cons(dirs[m1, mkdir(m7, md, # links(m1, dirs), m9, entries)], files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m1 ∈ dirs, m ∈ files, m ∈ icache, ∀ 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)) ⊦

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