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Proof step 114 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ icache-cons(icache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ 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 116:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ; valid-ino(ino, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ valid-inode(icache[ino].inode, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) )

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 [m, mkfile(m0, md, # links(m, dirs), content[pageno, buf]) ]] flags: <all paths>

Additional information

Used terms: icache, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]