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Proof step 349 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 350:
⊦ 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 351:
# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ ∀ ino. ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = ino ∧ (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty ⊃ valid-file-inode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ; valid-ino(ino, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ valid-inode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

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 [m0, mkientry (false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ], dirs, files0 [m0, mkfile (m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ]] flags: <all paths>

Additional information

Used terms: icache [m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ], dirs, files0 [m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ]