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Proof step 886 from proof refine-truncate-buff-none-uncached (previous step)

cache_icache[m1].inode.nlink = # links(m1, cache_dirs), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m2 / VFS_PAGE_SIZE ∈ content, m1 ∈ cache_files, key ∈ cache_pcache, m1 ∈ cache_icache, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key0. key0 ∈ cache_pcache → key0.data? ∧ # cache_pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ cache_files ∧ (¬ cache_pcache[key0].dirty → key0.part ∈ cache_files[key0.ino].content ∧ cache_pcache[key0].page = cache_files[key0.ino].content[key0.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?, cache_icache[m1].inode.directory, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 887:
cache_icache[m1].inode = mkinode(m0, md, boolvar, m4, m5, m6), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), ¬ boolvar, m4 = # links(m1, cache_dirs), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ 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_pcache), m1 ∈ cache_icache, key ∈ cache_pcache, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key0. key0 ∈ cache_pcache → key0.data? ∧ # cache_pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ cache_files ∧ (¬ cache_pcache[key0].dirty → key0.part ∈ cache_files[key0.ino].content ∧ cache_pcache[key0].page = cache_files[key0.ino].content[key0.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data?, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache[m1].inode, m0, md, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache[m1].inode, m0, md, boolvar, m4, m5, m6