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Proof step 798 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), # content0[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data?, ∀ key. key ∈ cache_pcache0 → key.data? ∧ # cache_pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ cache_files ∧ (¬ cache_pcache0[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache0[key].page = cache_files[key.ino].content[key.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 799:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 800:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), # content0[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m2 / VFS_PAGE_SIZE ∈ content1, m1 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ∧ # cache_pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ cache_files ∧ (¬ cache_pcache0[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache0[key].page = cache_files[key.ino].content[key.part]), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m1 ∈ cache_icache ∧ ¬ cache_icache[m1].inode.directory
Proof step 827:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), mkfile(cache_icache[m1].inode.size, cache_icache[m1].inode.meta, cache_icache[m1].inode.nlink, (cache_files ⊕ cache_pcache0)[m1].content) = mkfile(m0, md0, # links(m1, cache_dirs), content0), # content0[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m2 / VFS_PAGE_SIZE ∈ content1, m1 ∈ cache_files, m1 ∈ cache_icache, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ∧ # cache_pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ cache_files ∧ (¬ cache_pcache0[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache0[key].page = cache_files[key.ino].content[key.part]), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, cache_icache[m1].inode.directory, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [m1, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used terms: m1, cache_icache, cache_files ⊕ cache_pcache0