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Proof step 794 from proof refine-truncate-buff-none-uncached (previous step)

asynced0 ↔ m2 ≤ m ∧ old_ino ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, asynced0, buf-opt = none, content = content0, ino = m1, old_ino = m2 % VFS_PAGE_SIZE, pageno = m2 / VFS_PAGE_SIZE, size = min(m, m2), 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), m2 / VFS_PAGE_SIZE ∈ content1, m1 ∈ cache_files, pageno ∈ afs_files[ino].content, m2 ≤ m, m2 ≤ m → old_ino ≠ 0 → VFS_PAGE_SIZE ≠ 0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # afs_files[ino].content[pageno] ∧ pageno ∈ afs_files[ino].content ∧ VFS_PAGE_SIZE ≥ old_ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 795:
VFS_PAGE_SIZE = n0 + 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), # content0[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, 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), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)