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Proof step 103 from proof inv-writepage (previous step)

# 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), dcache-cons(dcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ dcache-cons(dcache, 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 104:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 105:
# 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])]), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])])

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache, dirs, files [m, mkfile(m0, md, # links(m, dirs), content[pageno, buf]) ]] flags: <all paths>

Additional information

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