[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 44 from proof read-loop-term (previous step)

VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), buf1 = copy(content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, buf, n6, min(n5, n7, m2 - n0 + n6)), err = ESUCCESS, inode = mkinode(m, md, boolvar, m0, m1, m2), ¬ isdir, n = n6 + min(n5, n7, m2 - n0 + n6), n1 = n5 + n0 + n6, m2 ≠ n0 + n6, n5 ≠ 0, n7 ≠ 0, n0 + n6 < m2, afs-cons(dirs, files), (n0 + n6) / VFS_PAGE_SIZE ∈ content, m ∈ files, n5 + n6 ≤ # buf, n6 ≤ # buf, n6 + min(n5, n7, m2 - n0 + n6) ≤ # buf, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7, m2 - n0 + n6) ≤ VFS_PAGE_SIZE, ∀ 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 ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err)⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), buf1 = copy(content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, buf, n6, min(n5, n7, n8)), err = ESUCCESS, inode = mkinode(m, md, boolvar, m0, m1, m2), ¬ isdir, m2 = n8 + n0 + n6, n = n6 + min(n5, n7, n8), n1 = n5 + n0 + n6, n0 + n6 < m2, afs-cons(dirs, files), m ∈ files, (n0 + n6) / VFS_PAGE_SIZE ∈ content, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7, n8) ≤ VFS_PAGE_SIZE, n6 + min(n5, n7, n8) ≤ # buf, n6 ≤ # buf, n5 + n6 ≤ # buf, n0 + n6 ≤ m2, ∀ 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 ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_read_block#(n0, n1, inode, dirs, files, asynced; buf1, n, isdir, err)⟫ true, m2 = n0 + n6, n5 = 0, n7 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0 + n6, m2, n8]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0 + n6, m2, n8