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Proof step 24 from proof write-loop-term (previous step)

files[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, ino = (ino2 + ino0) % VFS_PAGE_SIZE, ino0 = n6, ino1 = n5 + n0 + n6, ino2 = n0, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = min(ino1 - ino2 + ino0, VFS_PAGE_SIZE - ino), n1 = n5 + n0 + n6, pageno = (ino2 + ino0) / VFS_PAGE_SIZE, afs-cons(dirs, files), m ∈ files, n6 ≤ # buf, n5 + n6 ≤ # buf, VFS_PAGE_SIZE ≥ ino, ino1 ≥ ino2 + ino0, ∀ 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) ⊦ ⟪vfs_writepage#(inode, pageno, buf, ino0, ino, n, dirs; err, files, asynced); if err = ESUCCESS then ino0 := ino0 + n; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); n6 := ino0; while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf, n1, dirs; n6, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink), VFS_PAGE_SIZE = 0, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
files[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, min(n5, VFS_PAGE_SIZE - (n0 + n6) % VFS_PAGE_SIZE) ≠ 0, afs-cons(dirs, files), m ∈ files, n5 + n6 ≤ # buf, n6 ≤ # buf, ∀ 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) ⊦ ⟪vfs_writepage# (mkinode(m, md, false, # links(m, dirs), 0, m2), (n0 + n6) / VFS_PAGE_SIZE, buf, n6, (n0 + n6) % VFS_PAGE_SIZE, min(n5 + n0 + n6 - n0 + n6, VFS_PAGE_SIZE - (n0 + n6) % VFS_PAGE_SIZE), dirs ; err, files, asynced); n := min(n5 + n0 + n6 - n0 + n6, VFS_PAGE_SIZE - (n0 + n6) % VFS_PAGE_SIZE); ino0 := n6; if err = ESUCCESS then ino0 := ino0 + n; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); n := ino0; n1 := n5 + n0 + n6; isdir := false; while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink)

Rule argument

Additional information

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