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Proof step 36 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) + ((⌜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), ((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) + ((⌜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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
# σ = ∞, # buf0 = n4 + n0 + n1, ⌜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 n4)) + (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 n4)) + (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: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0 + n1, # buf0, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0 + n1, # buf0, n