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

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0 upto (m0 * VFS_PAGE_SIZE + n0)).stream from m0 * VFS_PAGE_SIZE + n0 = σ⊥), n0 ≠ 0 ∧ m0 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 103:
⊦ 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 104:
files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0 upto (m0 * VFS_PAGE_SIZE + n0)).stream from m0 * VFS_PAGE_SIZE + n0 = σ⊥), n0 ≠ 0 ∧ m0 ∈ content0, (m0 * VFS_PAGE_SIZE + n0 = m0 * VFS_PAGE_SIZE + n0 ∧ n0 ≠ 0 ∧ n0 < VFS_PAGE_SIZE) ∧ (true ↔ finp(content0.stream) → ⌜(m0 + 1) * VFS_PAGE_SIZE⌝ < # content0.stream ∨ ⌜(m0 + 1) * VFS_PAGE_SIZE⌝ = # content0.stream)
Proof step 110:
m0 * VFS_PAGE_SIZE + n0 = m0 * VFS_PAGE_SIZE + n0, files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0.stream to (m0 + 1) * VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n0 = σ⊥), n0 = 0, n0 ≠ 0 ∧ m0 ∈ 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] → [m0, n0, m0 * VFS_PAGE_SIZE + n0, content0] flags: <all paths>

Additional information

Used terms: m0, n0, m0 * VFS_PAGE_SIZE + n0, content0