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Proof step 138 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), afs_files0 = ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m1, mkfile (m0, md0, # links(m1, cache_dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, 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), m2 / VFS_PAGE_SIZE ∈ content0, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, VFS_PAGE_SIZE ≤ # content0[m2 / VFS_PAGE_SIZE], m2 ≤ m, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_inode_sync#(mkinode(m1, md, false, # links(m1, cache_dirs), 0, m); cache_dirs, afs_files0); inode := (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, afs_files0[m1].meta, false, afs_files0[m1].nlink, 0, afs_files0[m1].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs2 ∧ afs_files0 = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ truncate(m1, m2, cache_pcache0) [datakey(m1, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ]) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m))] ∧ ¬ asynced ∧ fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) = fill(((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ (m1 ∈ cache_dirs2 ⊃ mkinode(m1, cache_dirs2[m1].meta, true, cache_dirs2[m1].nlink, cache_dirs2[m1].nsubdirs, cache_dirs2[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), afs_files0 = ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m1, mkfile (m0, md0, # links(m1, cache_dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, m2 % VFS_PAGE_SIZE ≠ 0, 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), m2 / VFS_PAGE_SIZE ∈ content0, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, VFS_PAGE_SIZE ≤ # content0[m2 / VFS_PAGE_SIZE], m2 ≤ m, ¬ datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_inode_sync#(mkinode(m1, md, false, # links(m1, cache_dirs), 0, m); cache_dirs, afs_files0); inode := (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, afs_files0[m1].meta, false, afs_files0[m1].nlink, 0, afs_files0[m1].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs2 ∧ afs_files0 = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m1, m2, cache_pcache0) [datakey(m1, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ]) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m))] ∧ ¬ asynced ∧ fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) = fill(((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ (m1 ∈ cache_dirs2 ⊃ mkinode(m1, cache_dirs2[m1].meta, true, cache_dirs2[m1].nlink, cache_dirs2[m1].nsubdirs, cache_dirs2[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)