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Proof step 1022 from proof refine-truncate-buff-none-uncached (previous step)

cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), 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), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3, mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2))] = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1023:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 1024:
((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), 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), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, ∀ ino. ( ino ∈ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3, mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2))] ↔ ino ∈ (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))]) ∧ ( ino ∈ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3, mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2))] → ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3, mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2))][ino] = ( (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))] )[ino ]), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files, files0] → [((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2)) ], ( cache_files [m3, mkfile (m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2)) ] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache [m3, mkientry (false, mkinode (m3, md1, false, # links(m3, cache_dirs), 0, m6)) ]] flags: <all paths>

Additional information

Used terms: ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2)) ], ( cache_files [m3, mkfile (m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2)) ] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache [m3, mkientry (false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6)) ]