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Proof step 32 from proof writepage-prepost (previous step)

⌜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) + ⌜copy(buf1, m, 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) + ⌜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 cut formula

And obtained the following new goals

Proof step 33:
# 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)
Proof step 63:
⌜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 = ∞, (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)

Rule argument

fma: # σ = ∞

Additional information

Used formulas: # σ = ∞