[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 48 from proof writepage-prepost (previous step)

# 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 ⊦ #((⌜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 from n3 * VFS_PAGE_SIZE + n0 + n1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ m ≤ n ∧ ¬ # σ0 < ⌜n⌝ → (σ0 to n) from m = (σ0 from m) to (n - m)
Proof step 50:
# σ = ∞, # buf0 = n4 + 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 n3 * VFS_PAGE_SIZE from n0 + n1) to (VFS_PAGE_SIZE - n0 + n1)) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = σ from n3 * VFS_PAGE_SIZE + n0 + n1, #(σ from n3 * VFS_PAGE_SIZE) < ⌜VFS_PAGE_SIZE⌝

Rule argument

spec: stream, inst: buffer-inf name: swap-to-from seq: ⊦ m ≤ n ∧ ¬ # σ0 < ⌜n⌝ → (σ0 to n) from m = (σ0 from m) to (n - m) subst: [m, n, σ0] → [n0 + n1, VFS_PAGE_SIZE, σ from n3 * VFS_PAGE_SIZE] flags: <all paths>

Additional information

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