[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 16 from proof write-inv-post (previous step)

files1 -- ino = files0 -- ino, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), content0.stream from m1 = σ⊥, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ # splice(buf, 0, (content0.stream to m1).buf, n0, n) = (n ≠ 0 ∧ m1 < n0 + n ⊃ n0 + n;m1) ∧ ( n3 < # splice(buf, 0, (content0.stream to m1).buf, n0, n) → splice(buf, 0, (content0.stream to m1).buf, n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ m ≠ 0 → # splice(buf, n0, buf0, n1, m) = max(# buf0, n1 + m)
Proof step 18:
files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), content0.stream from m1 = σ⊥, n = 0, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ # splice(buf, 0, (content0.stream to m1).buf, n0, n) = (n ≠ 0 ∧ m1 < n0 + n ⊃ n0 + n;m1) ∧ ( n3 < # splice(buf, 0, (content0.stream to m1).buf, n0, n) → splice(buf, 0, (content0.stream to m1).buf, n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3])
Proof step 26:
files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), content0.stream from m1 = σ⊥, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ n = 0, max(# (content0.stream to m1).buf, n0 + n) = (n ≠ 0 ∧ m1 < n0 + n ⊃ n0 + n;m1) ∧ ( n3 < max(# (content0.stream to m1).buf, n0 + n) → splice(buf, 0, (content0.stream to m1).buf, n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3])

Rule argument

spec: array-splice, inst: buffer name: splice-len seq: ⊦ m ≠ 0 → # splice(buf, n0, buf0, n1, m) = max(# buf0, n1 + m) subst: [m, n1, buf0, n0, buf] → [n, n0, (content0.stream to m1).buf, 0, buf] flags: <all paths>

Additional information

Used terms: n, n0, (content0.stream to m1).buf, 0, buf