[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 21 from proof read-loop-term (previous step)

buf = mkbuf(VFS_PAGE_SIZE), buf0 = buf1, err = ESUCCESS, ino = (ino2 + ino0) % VFS_PAGE_SIZE, ino0 = n6, ino1 = n5 + n0 + n6, ino2 = n0, inode = mkinode(m, md, boolvar, m0, m1, m2), ¬ isdir, n = min(ino1 - ino2 + ino0, VFS_PAGE_SIZE - ino, inode.size - ino2 + ino0), n1 = n5 + n0 + n6, pageno = (ino2 + ino0) / VFS_PAGE_SIZE, afs-cons(dirs, files), m ∈ files, n0 + n6 ≤ m2, n6 ≤ # buf1, n5 + n6 ≤ # buf1, inode.size ≥ ino2 + ino0, VFS_PAGE_SIZE ≥ ino, ino1 ≥ ino2 + ino0, ∀ n2, n3, n4, err, inode, m, md, boolvar, m0, m1, m2, isdir, dirs, files, buf, asynced. n2 - n3 + n4 < n5 → err = ESUCCESS ∧ inode = mkinode(m, md, boolvar, m0, m1, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ m2 ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err)⟫ true ⊦ ⟪afs_readpage#(inode, pageno, dirs, files, asynced; buf, err); if err = ESUCCESS then {buf0 := copy(buf, ino, buf0, ino0, n); ino0 := ino0 + n}; inode := mkinode(m, md, boolvar, m0, m1, m2); n6 := ino0, buf1 := buf0; while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n6, isdir, err)⟫ true, VFS_PAGE_SIZE = 0, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
buf = mkbuf(VFS_PAGE_SIZE), err = ESUCCESS, VFS_PAGE_SIZE - (n0 + n6) % VFS_PAGE_SIZE ≠ 0, m2 ≠ n0 + n6, n5 ≠ 0, n0 + n6 < m2, afs-cons(dirs, files), m ∈ files, n6 ≤ # buf1, n5 + n6 ≤ # buf1, ∀ n2, n3, n4, err, inode, m, md, boolvar, m0, m1, m2, isdir, dirs, files, buf, asynced. n2 - n3 + n4 < n5 → err = ESUCCESS ∧ inode = mkinode(m, md, boolvar, m0, m1, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ m2 ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err); while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n3, n2, inode, dirs, files, asynced; buf, n4, isdir, err)⟫ true ⊦ ⟪afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), (n0 + n6) / VFS_PAGE_SIZE, dirs, files, asynced; buf, err); n := min(n5 + n0 + n6 - n0 + n6, VFS_PAGE_SIZE - (n0 + n6) % VFS_PAGE_SIZE, m2 - n0 + n6); ino0 := n6; buf0 := buf1; if err = ESUCCESS then {buf0 := copy(buf, (n0 + n6) % VFS_PAGE_SIZE, buf0, ino0, n); ino0 := ino0 + n}; inode := mkinode(m, md, boolvar, m0, m1, m2); n := ino0, buf1 := buf0; n1 := n5 + n0 + n6; isdir := false; while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err)⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%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)% ⊦ m ≤ n → (n - m = 0 ↔ n = m); (s)% ⊦ min(n0, n1, n2) = 0 ↔ n0 = 0 ∨ n1 = 0 ∨ n2 = 0; (ws)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (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)