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Proof step 55 from proof writepage-prepost (previous step)

# buf0 = n4 + n0 + n1, # σ = ∞, VFS_PAGE_SIZE = n5 + n0 + n1, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1 ⊦ #((⌜buf1⌝ from m) to n1) = ∞, ((σ from n3 * VFS_PAGE_SIZE + n0 + n1) to n5) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = σ from n3 * VFS_PAGE_SIZE + n0 + n1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ # σ0 = ∞ → ((σ0 to n) + σ1 = σ0 ↔ σ1 = σ0 from n)
Proof step 57:
# σ = ∞, # buf0 = n4 + n0 + n1, #(σ from n3 * VFS_PAGE_SIZE + n0 + n1) = ∞, VFS_PAGE_SIZE = n5 + n0 + n1, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ #((⌜buf1⌝ from m) to n1) = ∞, σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE = σ from n3 * VFS_PAGE_SIZE + n0 + n1 from n5

Rule argument

spec: buffer-inf-conv name: split-prefix-append-to seq: ⊦ # σ0 = ∞ → ((σ0 to n) + σ1 = σ0 ↔ σ1 = σ0 from n) subst: [σ1, n, σ0] → [σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE, n5, σ from n3 * VFS_PAGE_SIZE + n0 + n1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # σ0 = ∞ → #(σ0 from n) = ∞; (s) Used terms: σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE, n5, σ from n3 * VFS_PAGE_SIZE + n0 + n1