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Proof step 615 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(m10, md3, m11, content), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))][ino] = mkientry(boolvar0, mkinode(m4, md1, false, m7, m8, m9)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), ino = m3, 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[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))], m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_files, 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 (m9, md1, m7, 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))]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 616:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[m4] = mkfile(m1, md2, # links(m4, cache_dirs), content1), cache_icache[m4] = mkientry(boolvar, mkinode(m0, md0, false, # links(m4, cache_dirs), m5, m6)), 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), m4 ∈ cache_icache, m4 ∈ cache_files, m2 ≤ m9, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, mkfile (m9, md1, # links(m4, cache_dirs), (content1 ⊕ mkcontent(m4, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) = mkfile (m9, md1, # links(m4, cache_dirs), (content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ⊕ mkcontent (m4, truncate(m4, m2, cache_pcache0)[datakey(m4, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)