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Proof step 33 from proof writepage-prepost (previous step)

# σ = ∞, ⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE)) * F))(files0), ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ n0 + m ≤ # buf0 ∧ n1 + m ≤ # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ = (⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + ((⌜buf1⌝ from n1 + m) to (# buf1 - n1 + m))
Proof step 35:
# σ = ∞, ⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), (( m0 =>mkfile (n2, md, m1, (σ to n3 * VFS_PAGE_SIZE) + ((⌜buf0⌝ to n0) + ((⌜buf1⌝ from m) to n1) + ((⌜buf0⌝ from n0 + n1) to (# buf0 - n0 + n1))) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) ) * F) )(files0), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0 ⊦ (σ to n3 * VFS_PAGE_SIZE) + ((⌜buf0⌝ to n0) + ((⌜buf1⌝ from m) to n1) + ((⌜buf0⌝ from n0 + n1) to (# buf0 - n0 + n1))) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)

Rule argument

spec: afs-stream name: copy-stream-append seq: ⊦ n0 + m ≤ # buf0 ∧ n1 + m ≤ # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ = (⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + ((⌜buf1⌝ from n1 + m) to (# buf1 - n1 + m)) subst: [m, n1, buf1, n0, buf0] → [n1, n0, buf0, m, buf1] flags: <all paths>

Additional information

Used terms: n1, n0, buf0, m, buf1