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Proof step 105 from proof truncate-empty (previous step)

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0 upto m0 * VFS_PAGE_SIZE).stream from m0 * VFS_PAGE_SIZE = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 106:
⊦ n = n0 * VFS_PAGE_SIZE → (content upto n).stream = (content.stream to n0 * VFS_PAGE_SIZE) + σ⊥
Proof step 107:
m0 * VFS_PAGE_SIZE = m0 * VFS_PAGE_SIZE, files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0.stream to m0 * VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE = σ⊥)

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] → [m0, m0 * VFS_PAGE_SIZE, content0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m⌝ < ∞; (s) Used terms: m0, m0 * VFS_PAGE_SIZE, content0