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Proof step 87 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_pcache[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files [m3, cache_files [m3, cache_files [m3, mkfile(m1, md2, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m3 ] .size:= m6 ] [m3 ] .meta:= md1 ] [m3 ] = mkfile(m, md, m4, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m2 ≤ m6, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set#(mkinode(m3, md, false, m4, 0, m), false; err, cache_icache); pcache_truncate#(m3, m2, m6; err, cache_pcache); inode1 := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, md, false, m4, 0, m) ); buf-opt1 := some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)); asynced1 := true; if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt1.buf, false; err, cache_pcache); if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt1 := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_truncate#(m6, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m3, mkfile(m6, md1, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_pcache[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set#(mkinode(m3, md, false, # links(m3, cache_dirs), 0, m), false; err, cache_icache); pcache_truncate#(m3, m2, m; err, cache_pcache); inode1 := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) ); buf-opt1 := some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)); asynced1 := true; if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt1.buf, false; err, cache_pcache); if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt1 := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_truncate#(m, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)