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Proof step 1055 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]) = mkfile(m8, md3, m9, content), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar, mkinode(m, md, false, m4, m5, m7)), ((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), cache_icache[m3] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), buf-opt0.some?, 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), ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], m3 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2));((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino]) = mkfile(m7, md, m4, content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m3 ∈ cache_icache ∧ ¬ boolvar0, m3 ∈ cache_icache ∧ boolvar0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1056:
⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]
Proof step 1057:
# buf-opt0.buf = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]) = mkfile(m8, md3, m9, content), cache_icache[m3] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (cache_files ⊕ cache_pcache0)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar, mkinode(m, md, false, m4, m5, m7)), buf-opt0.some?, 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, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2));((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino]) = mkfile(m7, md, m4, content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m3 ∈ cache_icache, m3 ∈ cache_icache ∧ boolvar0, m3 ∈ cache_icache ∧ ¬ boolvar0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: cache-base name: at-icache-overwrite-not-cached seq: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [m3, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used terms: m3, cache_icache, cache_files ⊕ cache_pcache0