[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 99 from proof truncate-greater (previous step)

files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n0 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0 upto (m1 * VFS_PAGE_SIZE + n1)).stream to n0 + m1 * VFS_PAGE_SIZE + n1 = (content0.stream to m1 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0)), n1 ≠ 0 ∧ m1 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 100:
⊦ n = n0 * VFS_PAGE_SIZE + n1 ∧ n1 ≠ 0 ∧ n1 < VFS_PAGE_SIZE → (content upto n).stream = (content.stream to (n0 + 1) * VFS_PAGE_SIZE) + σ⊥
Proof step 101:
files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0 upto (m1 * VFS_PAGE_SIZE + n1)).stream to n0 + m1 * VFS_PAGE_SIZE + n1 = (content0.stream to m1 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0)), n0 = 0, n1 ≠ 0 ∧ m1 ∈ content0, (m1 * VFS_PAGE_SIZE + n1 = m1 * VFS_PAGE_SIZE + n1 ∧ n1 ≠ 0 ∧ n1 < VFS_PAGE_SIZE) ∧ (true ↔ finp(content0.stream) → ⌜(m1 + 1) * VFS_PAGE_SIZE⌝ < # content0.stream ∨ ⌜(m1 + 1) * VFS_PAGE_SIZE⌝ = # content0.stream)
Proof step 107:
m1 * VFS_PAGE_SIZE + n1 = m1 * VFS_PAGE_SIZE + n1, files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0.stream to (m1 + 1) * VFS_PAGE_SIZE) + σ⊥ to n0 + m1 * VFS_PAGE_SIZE + n1 = (content0.stream to m1 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0)), n0 = 0, n1 = 0, n1 ≠ 0 ∧ m1 ∈ content0

Rule argument

spec: afs-stream name: content-trunc seq: ⊦ n = n0 * VFS_PAGE_SIZE + n1 ∧ n1 ≠ 0 ∧ n1 < VFS_PAGE_SIZE → (content upto n).stream = (content.stream to (n0 + 1) * VFS_PAGE_SIZE) + σ⊥ subst: [n0, n1, n, content] → [m1, n1, m1 * VFS_PAGE_SIZE + n1, content0] flags: <all paths>

Additional information

Used terms: m1, n1, m1 * VFS_PAGE_SIZE + n1, content0