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Proof step 197 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ;cache_files[ino] ) = mkfile(m11, md3, m12, content), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, (∅)[m3] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar2, mkinode(m0, md0, true, m8, m9, m10)), 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, md, false, # links(m3, cache_dirs), 0, m))], m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, (ino = m3 ⊃ mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ;((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] ) = mkfile (m11, md3, m12, content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), ino = m3, m3 ∈ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 198:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[ino] = mkfile(m11, md3, # links(ino, cache_dirs), content), (∅)[m3] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar2, mkinode(m0, md0, true, m8, m9, m10)), 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_icache, ino ∈ cache_files, m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] = mkfile (m11, md3, # links(ino, cache_dirs), content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), m3 ∈ cache_icache

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)