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Proof step 38 from proof truncate-smaller (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files0), m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files0 ⊦ [asynced := ?] (content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)].stream to m2 = content0.stream to m2)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
VFS_PAGE_SIZE = n0 + n1, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), m2 = m1 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] (content0[m1, fill(content0[m1], zero, n1, n0)].stream to m2 = content0.stream to m2), 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, m2, m1, n]

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, m2, m1, n