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Proof step 1038 from proof refine-truncate-buff-none-uncached (previous step)

(∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), 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), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), 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, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, mkfile(m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache0)) = mkfile(m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), ino ∈ cache_icache, 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 1039:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 1040:
cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), ((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), (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), 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), ino ∈ cache_files, m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, ino ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m8 = m8 ∧ md1 = md1 ∧ # links(ino, cache_dirs) = # links(ino, cache_dirs) ∧ content ⊕ mkcontent(ino, cache_pcache0) = content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [m, md, m0, content, m1, md0, m2, content0] → [m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache0), m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))] flags: <all paths>

Additional information

Used terms: m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache0), m8, md1, # links(ino, cache_dirs), content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))