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Proof step 22 from proof write-inv-rec (previous step)

n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, content0.stream = (content.stream to n0) + (⌜buf⌝ to n) + (content.stream from n0 + n), VFS_PAGE_SIZE = n3 + 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, n2 + m ≤ VFS_PAGE_SIZE, m + n2 ≤ VFS_PAGE_SIZE, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf ⊦ (content0.stream to m0 * VFS_PAGE_SIZE) + (⌜getpage(m0, content0)⌝ to n2) + ((⌜buf⌝ from n) to m) + ((⌜getpage(m0, content0)⌝ from n2 + m) to n3) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), n3 + m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ # getpage(n, content) = VFS_PAGE_SIZE → ⌜getpage(n, content)⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE
Proof step 24:
# getpage(m0, content0) = VFS_PAGE_SIZE, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, content0.stream = (content.stream to n0) + (⌜buf⌝ to n) + (content.stream from n0 + n), VFS_PAGE_SIZE = n3 + 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, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, n2 + m ≤ VFS_PAGE_SIZE ⊦ n3 + m = 0, (content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n2) + ((⌜buf⌝ from n) to m) + ((((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from n2 + m) to n3) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

spec: afs-stream name: content-read seq: ⊦ # getpage(n, content) = VFS_PAGE_SIZE → ⌜getpage(n, content)⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE subst: [content, n] → [content0, m0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, m0, content) → # getpage(n, content) = VFS_PAGE_SIZE; (s) Used terms: content0, m0