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Proof step 208 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons (dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), key ∈ pcache, m0 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 209:
⊦ 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 210:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % 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(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), dcache-cons(dcache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, key ∈ pcache, m2 ≤ m, asynced1 → synced(files0, icache, pcache), ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files0) ;valid-ino(ino, dirs, files0) ∧ valid-inode(icache[ino].inode, dirs, files0) ) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?

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, files0] flags: <all paths>

Additional information

Used terms: icache, dirs, files0