[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 79 from proof write-inv-rec (previous step)

n0 + n = m0 * (n4 + n2 + m) + n2, (n4 + n2 + m) * m0 + n4 + n2 + m = n3 + m0 * (n4 + n2 + m) + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), n2 < n4 + n2 + m, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * (n4 + n2 + m) ≤ n3 + m0 * (n4 + n2 + m) + n2, m0 * (n4 + n2 + m) ≤ # buf + n0, m + n2 ≤ n4 + n2 + m, m0 * (n4 + n2 + m) + n2 ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * (n4 + n2 + m) ≤ m0 * (n4 + n2 + m) + n2, m0 * (n4 + n2 + m) ≤ n1, n2 + m ≤ n4 + n2 + m ⊦ n4 + m = 0, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * (n4 + n2 + m)) + (((content.stream to n0) + (⌜buf⌝ to n) to m0 * (n4 + n2 + m) + n2) from m0 * (n4 + n2 + m)) + ((⌜buf⌝ from n) to m) + ((content.stream from (m0 * (n4 + n2 + m) + n2) + m) to n4) + (content.stream from (m0 * (n4 + n2 + m) + n2) + n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

User applied rule simplifier

And obtained the following new goals

Proof step 80:
n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ # buf + n0, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n1 ⊦ n4 + m = 0, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) + ((content.stream from (n0 + n) + m) to n4) + (content.stream from (n0 + n) + n4 + m) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (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)%mult-c: ⊦ m * n = n * m; from specification nat-mult