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Proof step 39 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n0 + n % VFS_PAGE_SIZE, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files1), n / VFS_PAGE_SIZE ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ((content0[n / VFS_PAGE_SIZE, fill(content0[n / VFS_PAGE_SIZE], zero, n % VFS_PAGE_SIZE, n0)] upto n).stream from n = σ⊥)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n = m0 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ((content0[m0, fill(content0[m0], zero, n1, n0)] upto n).stream from n = σ⊥), VFS_PAGE_SIZE = 0, n1 = 0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [n, m, m0, n0] → [VFS_PAGE_SIZE, n, m0, n1]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: VFS_PAGE_SIZE, n, m0, n1