[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 85 from proof write-inv-rec (previous step)

n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ # buf + n0, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n1 ⊦ #(((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) = ∞, #((⌜buf⌝ from n) to m) = ∞, n4 + m = 0, ((content.stream from (n0 + n) + m) to n4) + (content.stream from (n0 + n) + n4 + m) = content.stream from n0 + n + m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ # σ0 = ∞ → ((σ0 to n) + σ1 = σ0 ↔ σ1 = σ0 from n)
Proof step 87:
#(content.stream from (n0 + n) + m) = ∞, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, m0 * VFS_PAGE_SIZE ≤ n1, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m0 * VFS_PAGE_SIZE ≤ # buf + n0 ⊦ #((⌜buf⌝ from n) to m) = ∞, #(((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) = ∞, n4 + m = 0, content.stream from (n0 + n) + n4 + m = content.stream from (n0 + n) + m from n4

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] → [content.stream from (n0 + n) + n4 + m, n4, content.stream from (n0 + n) + m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(content.stream from n) = ∞; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: content.stream from (n0 + n) + n4 + m, n4, content.stream from (n0 + n) + m