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Proof step 42 from proof writepage-prepost (previous step)

# σ = ∞, # buf0 = n4 + n0 + n1, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0, n0 ≤ VFS_PAGE_SIZE ⊦ (σ to n3 * VFS_PAGE_SIZE) + ((σ from n3 * VFS_PAGE_SIZE) to n0) + ((⌜buf1⌝ from m) to n1) + (((σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from 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), #(σ from n3 * VFS_PAGE_SIZE) < ⌜VFS_PAGE_SIZE⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# buf0 = n4 + n0 + n1, # σ = ∞, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ (σ to n3 * VFS_PAGE_SIZE) + ((σ from n3 * VFS_PAGE_SIZE) to n0) + ((⌜buf1⌝ from m) to n1) + (((σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from 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

Additional information

Used simplifier rules: ⊦ ¬ ∞ < n∞; (s)% ⊦ # σ0 = ∞ → #(σ0 from n) = ∞; (s)