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Proof step 102 from proof truncate-greater (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 103:
⊦ n = n0 * VFS_PAGE_SIZE → (content upto n).stream = (content.stream to n0 * VFS_PAGE_SIZE) + σ⊥
Proof step 104:
m1 * VFS_PAGE_SIZE = m1 * VFS_PAGE_SIZE, files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0.stream to m1 * VFS_PAGE_SIZE) + σ⊥ to n0 + m1 * VFS_PAGE_SIZE = (content0.stream to m1 * VFS_PAGE_SIZE) + (σ⊥ to n0)), n0 = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m⌝ < ∞; (s) Used terms: m1, m1 * VFS_PAGE_SIZE, content0