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Proof step 5 from proof read-inv-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ read-inv(n0, n1, buf0, buf1, n, content) ↔ ⌜buf1⌝ = ((content.stream from n0) to n) + (⌜buf0⌝ from n)
Proof step 7:
# buf0 = # buf1, VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), ⌜buf1⌝ = ((content.stream from n0) to n) + (⌜buf0⌝ from n), afs-cons(dirs, files), ino ∈ files, n3 + n ≤ # buf1 ⊦ ⌜copy(getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, buf1, 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: <toplevel> name: read-inv seq: ⊦ read-inv(n0, n1, buf0, buf1, n, content) ↔ ⌜buf1⌝ = ((content.stream from n0) to n) + (⌜buf0⌝ from n) subst: [content, n, buf1, buf0, n1, n0] → [content, min(n3, n2, n1) + n, copy (getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, buf1, n, min(n3, n2, n1)), buf0, n3 + n0 + n, n0] flags: <all paths>

Additional information

Used terms: content, min(n3, n2, n1) + n, copy (getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, buf1, n, min(n3, n2, n1)), buf0, n3 + n0 + n, n0