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Proof step 76 from proof write-loop-term (previous step)

VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files0[m] = mkfile(m0, md1, # links(m, dirs), content0), dirs[m] = mkdir(m6, md3, m7, m8, entries), err = ESUCCESS, files = files0 [m, mkfile (m0, md1, # links(m, dirs), content0[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content0[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, # content0[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content0[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))][n2] ≠ VFS_PAGE_SIZE, min(n5, n7) ≠ 0, afs-cons(dirs, files0), ROOT_INO ∈ dirs, (n0 + n6) / VFS_PAGE_SIZE ∈ content0, m ∈ files0, n2 ∈ content0[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content0[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))], n6 ≤ # buf1, n5 + n6 ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n6 + min(n5, n7) ≤ # buf1, min(n5, n7) ≤ n5, ¬ m ∈ dirs, ∀ n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced. n2 - n3 + n4 < n5 → files[m] = mkfile(m1, md0, # links(m, dirs), content) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n3, inode, buf, n2, dirs; n4, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink) ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: n2 = (n0 + n6) / VFS_PAGE_SIZE

Additional information

Used simplifier rules: ⊦ n ≠ n0 → content[n0, buf][n] = content[n]; (s)% ⊦ n ≠ n0 → (n ∈ content[n0, buf] ↔ n ∈ content); (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ content[n, buf][n] = buf; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s) Used formulas: n2 = (n0 + n6) / VFS_PAGE_SIZE