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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ (m + n0) + n1 = m + n0 + n1
Proof step 58:
VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE = n3 + n0 + n, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n2 + m ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ n1, m0 * VFS_PAGE_SIZE ≤ n + n0, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ # buf + n0, m0 * VFS_PAGE_SIZE ≤ n3 + n0 + n ⊦ ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) to n2) + ((⌜buf⌝ from n) to m) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from (m0 * VFS_PAGE_SIZE + n2) + m) to n4) + (content.stream from n0 + n from n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), n4 + m = 0, #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) < ⌜VFS_PAGE_SIZE⌝ , #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from (m0 * VFS_PAGE_SIZE + n2) + m) < ⌜n4⌝

Rule argument

spec: nat-basic name: a seq: ⊦ (m + n0) + n1 = m + n0 + n1 subst: [n1, n0, m] → [m, n2, m0 * VFS_PAGE_SIZE] flags: <rotated> <all paths>

Additional information

Used terms: m, n2, m0 * VFS_PAGE_SIZE