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Proof step 41 from proof truncate-greater (previous step)

VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), m3 % VFS_PAGE_SIZE ≠ 0, n1 ≠ 0, afs-cons(dirs, files0), m3 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files0 ⊦ [asynced := ?] ( (content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3).stream to n1 + m3 = (content0.stream to m3) + (σ⊥ to n1))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
VFS_PAGE_SIZE = n0 + n2, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), m3 = m1 * VFS_PAGE_SIZE + n2, n2 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m0 ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ((content0[m1, fill(content0[m1], zero, n2, n0)] upto m3).stream to n1 + m3 = (content0.stream to m3) + (σ⊥ to n1)), VFS_PAGE_SIZE = 0, n1 = 0, n2 = 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, m3, 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, m3, m1, n