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Proof step 13 from proof read-inv-rec (previous step)

# buf0 = # buf1, # buf1 = n4 + n + min(n3, n2, n1), VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), afs-cons(dirs, files), ino ∈ files, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n2, n1) ≤ # buf1, n3 + n ≤ # buf1 ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((⌜getpage((n0 + n) / VFS_PAGE_SIZE, content)⌝ from (n0 + n) % VFS_PAGE_SIZE) to min(n3, n2, n1)) + (((content.stream from n0) to n) + (⌜buf0⌝ from n) from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ # getpage(n, content) = VFS_PAGE_SIZE → ⌜getpage(n, content)⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE
Proof step 15:
# buf1 = n4 + n + min(n3, n2, n1), # buf0 = # buf1, # getpage((n0 + n) / VFS_PAGE_SIZE, content) = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), afs-cons(dirs, files), ino ∈ files, n3 + n ≤ # buf1, n + min(n3, n2, n1) ≤ # buf1, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2, n1) ≤ VFS_PAGE_SIZE ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((((content.stream from (n0 + n) / VFS_PAGE_SIZE * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from (n0 + n) % VFS_PAGE_SIZE) to min(n3, n2, n1)) + (((content.stream from n0) to n) + (⌜buf0⌝ from n) from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n)

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] → [content, (n0 + n) / VFS_PAGE_SIZE] 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: content, (n0 + n) / VFS_PAGE_SIZE